fig1 shows a midsole 10 of the present invention in its preferred environment as a midsole for an athletic shoe 12 to be worn by a runner or the like . typically , the shoe 12 is attached to the runner &# 39 ; s foot by a lacing system 14 . with reference to fig2 - 8 , a preferred embodiment of the midsole 10 is shown as a one - piece , injection - molded elastomer having a top surface 16 , a bottom surface 18 , and a plurality of structural webs 20 that extend between the top surface 16 and the bottom surface 18 . preferably , the structural webs 20 form a tubular structure that is integrally formed with the top and bottom surfaces . conceptually , the midsole 10 can be divided into a forefoot section 22 and a heel section 24 . preferably , the structural webs 20 along the heel section 24 form heel tubes 26 that extend inward from a medial edge 28 and from a lateral edge 30 . as best shown in fig4 a preferred embodiment of the present invention has discontinuous heel tubes 26 that extend from the medial and lateral edges 28 and 30 , respectively , toward a central region 32 of the midsole having no tubes therein . the central region is bounded by heel tubes 26 , bottom surface 18 and top surface 16 . further , in the heel section 24 , the bottom surface 18 forms a &# 34 ; u &# 34 ;- shaped surface having legs 34 and 36 that extend from a rear tip 38 of the midsole toward the forefoot section 22 . associated with each leg 34 , 36 is a width 34 &# 39 ;, 36 &# 39 ;, the significance of which will be explained below . other embodiments of the heel section 24 may include heel tubes 26 that are continuous between the medial and lateral edges 28 , 30 , in which the case the bottom surface 18 would extend substantially over the heel section 24 and there would be no tubeless central region 32 . the forefoot section 22 similarly comprises the integrally formed top surface 16 , bottom surface 18 and intermediate structural webs 20 . as with the heel section , the structural webs 20 preferably form elongate tubular members 40 , hereinafter referred to as the forefoot tubes 40 . in the preferred embodiment the forefoot tubes 40 have slit - shaped openings 42 that extend along the length of the forefoot tubes . the openings 42 permit substantial longitudinal flexibility in the forefoot section 22 . in fig6 the midsole 10 is shown with the forefoot section 22 flexed , and the slit openings 42 are shown spread open from their relaxed state . substantial flexibility of the forefoot section along its longitudinal direction is a desirable property so that the athletic shoe 12 does not inhibit the natural tendency of the foot to roll from the heel onto the ball of the foot and onto the toe for push - off as the runner goes through a stride . the bottom surface is discontinuous at the openings 42 . in a preferred embodiment shown in fig4 the forefoot tubes 40 extend continuously from the medial edge 28 to the lateral edge 30 . in an alternative embodiment , shown in fig9 the forefoot tubes 40 are discontinuous between the medial and lateral edges , thereby forming a central forefoot region 44 having no tubes therein . the bottom surface 18 forms a &# 34 ; u &# 34 ;- shaped surface around the central forefoot region 44 thus forming legs 46 and 48 having widths 46 &# 39 ; and 48 &# 39 ;, respectively . the significance of the leg widths 46 &# 39 ;, 48 &# 39 ; will be explained below . by forming the tubeless central forefoot region , the forefoot section becomes more flexible laterally . preferably , the entire midsole is injection molded as one integral piece of an elastomer having a tensile characteristic such that the ratio of plastic strain to elastic strain is greater than 1 . 5 to 1 . one such elastomer is a copolyester polymer elastomer manufactured and sold by e . i . dupont de nemours under the trademark hytrel . hytrel is reasonably inert and significantly , it is quite durable . moreover , hytrel is not subject to tear propagation even when made in relatively thin cross - sections . the preferred embodiments of the midsole use dupont &# 39 ; s hytrel composition number 5556 . for a more complete description of this elastomer , see u . s . pat . no . 4 , 198 , 037 and references cited therein . u . s . pat . no . 4 , 198 , 037 is hereby incorporated herein by reference . as noted , the midsole 10 is preferably injection molded of hytrel . it is well known that hytrel will take a compression set . for this reason , the midsole of the present invention is molded into a preform and is subsequently compressed to take that set . as is taught in u . s . pat . no . 5 , 280 , 890 , compression of the hytrel material also results in orientation of the molecular structure and enhances the spring characteristics of the material . the effect of this compression is illustrated in fig7 and 8 . fig7 illustrates the preform configuration , wherein the heel tubes 26 have been preformed into an oval cross - section so the tubes 26 are &# 34 ; tall ,+ thereby providing a greater separation between the top surface 16 and the bottom surface 18 . after the preform has been removed from the mold and annealed at room temperature for up to 24 hours . it is then compressed , preferably to a solid position . that is , the top surface 16 is pressed toward the bottom surface 18 thus radially compressing the heel tubes 26 and forefoot tubes 40 . the midsole is compressed until it is &# 34 ; solid ,&# 34 ; wherein further force will not further move the surfaces together . upon release of the compressive force , the tubes 26 , 40 will partially spring back to a somewhat circular configuration as shown in fig8 . the midsole takes a &# 34 ; set &# 34 ; in this position . thereafter , the tubes 26 , 40 may be partially compressed during use by the runner , but as the runner &# 39 ; s weight is removed , the springs will completely return to their set configuration , such as is shown in fig8 . a complete description of the compression set procedure is provided in u . s . pat . no . 5 , 280 , 890 , which is hereby incorporated by reference . the heel tubes 26 and the forefoot tubes 40 have the characteristics of springs and therefore have a measurable spring constant . it has not yet been determined whether the spring constant for the tubes of the present invention is a constant , or a function of the amount of compressive travel of the tubes . furthermore , it has not yet been determined what the proper spring constant would be for the various configurations disclosed herein . however , it is known that various modifications to the configurations disclosed herein will affect the spring constant of the so that the midsole 10 can be designed for particular types and weights of runners after empirical data has been collected . the spring constant of the tubes can be increased by providing a longer tube . when the midsole 10 is loaded , the surfaces 16 , 18 will move towards one another , thereby radially compressing the tubes under the given load . obviously , a one - inch tube will radially compress more than a two - inch tube in length under the same load . thus , the longer tube will have a higher spring constant . in the context of an athletic shoe , the higher spring constant means that the tube will provide greater stability but less cushioning . the tubes 26 , 40 have wall thicknesses 50 and 52 , respectively which also affect the spring constants . a thicker wall thickness 50 or 52 will produce a higher spring constant . in the preferred embodiment of the present invention , the wall thickness of a particular heel tube 26 is constant along the length of the tube . the wall thickness of the forefoot tubes 40 varies between the medial edge 28 and the lateral edge 30 , preferably in a step - wise fashion , wherein the wall thickness would be a constant along a portion of the forefoot tube 40 , and the wall thickness would jump to a different thickness at some point along the length of the tube . alternatively , it is envisioned that any of the tubes could be provided with a tapering wall thickness wherein the wall thickness changes gradually from one end to the other of a particular tube . the preferred embodiment includes a two - stage spring constant in the heel section 24 . the heel tubes 26 have a spacing 27 between the opposite walls of adjacent tubes . the spacing 27 is chosen so that those opposing walls touch as the tubes 26 are compressed . further compression causes the tubes to press against each other thereby limiting the motion of the tube walls and changing the spring constant for further loading . thus , the heel tubes 26 have an initial spring constant at the onset of compression and after the opposing walls of adjacent tubes make contact , the tubes have a different , higher spring constant . it is envisioned that the ability to control the spring constants can be used in various combinations to precisely control the performance characteristics of the midsole . for example , in a preferred embodiment of the present invention , the heel tubes 26 are provided with a constant wall thickness , but the width 36 &# 39 ; of the lateral leg 36 could be less than the corresponding width 34 &# 39 ;, thereby placing shorter tubes 26 on the lateral side 30 as compared to the tubes on the medial side 28 . this configuration would create a shoe having a higher spring constant along its medial edge to resist over pronation . in a preferred embodiment , the width 36 &# 39 ; is approximately 24 mm and the width 34 &# 39 ; is approximately 26 mm . furthermore , the spring constant of the forefoot tubes 40 may be tailored by providing thicker wall sections in the tubes 40 in the regions proximate the medial edge 30 as compared to the wall thickness of the tubes 40 in the region close to the lateral edge 28 . the varying wall thicknesses can be incorporated into the embodiments shown in fig4 and fig9 . as is shown in fig5 the heel tubes 26 are provided with beveled ends 26 &# 39 ; so that the transverse width of the bottom surface 18 is greater than the transverse width of the top surface 16 at any particular point along the longitudinal length of the midsole 10 . by providing a wider bottom surface , the midsole is able to provide greater stability for the athletic shoe 12 . in the preferred embodiment of the present invention , the midsole 10 is provided with an outer sole 54 , which is affixed to the bottom surface 18 . preferably , the outer sole 54 is made of a material having a high scuff resistance and substantial durability . preferably , the outer sole 54 is provided with expansion joints 56 that cover one or more of the slit openings 42 , thereby allowing the forefoot section to flex and permitting the slit openings to expand . an alternative embodiment may include the midsole of the present invention fabricated into two sections . as shown in fig1 , the two sections would comprise a forefoot section 58 and a rearfoot section 60 . making the midsole 10 into two sections provides numerous advantages . it may be possible to cut down on the number of molds necessary to provide midsoles for the full range of shoe sizes . for example , it may be possible to provide three different sizes of heel sections 60 , while providing five different sizes of forefoot sections 58 . the various sections can be mixed to provide the full range of shoe sizes . also , by providing a midsole in two sections , it is possible to design sections to meet specific performance requirements . for example , a rearfoot section 60 may be designed for a size 9 , 150 - pound runner having a substantial over pronation problem , and another heel section 60 may be designed for a size 9 , 150 - runner who under pronates . likewise , the spring constants in the forefoot section 58 can be specifically tailored to different runners and performance characteristics . the optimum values for the design parameters stated herein will be determined after extensive empirical data is collected . at present , the specific design parameters , such as , for example , optimum heel tube thickness and length for an over - pronating , 150 pound runner are unknown , and it is envisioned that physical testing will be necessary to determine such parameters . numerous characteristics and advantages of the invention have been set forth in the foregoing description , together with details of the structure and function of the invention . the novel features hereof are pointed out in the appended claims . the disclosure is illustrative only , and changes may be made in detail , especially in matters of shape , size , and arrangement of parts within the principle of the invention to the full extent indicated by the broad general meaning of the terms in the claims .