a gripping inflatable packer having an elastomeric bladder expandable to sealingly engage the outer surface thereof against the wall surface of the well bore to effectively inhibit the passage of well fluid through the well bore . the gripping inflatable packer has an elastomeric bladder with an outer surface sized and shaped to provide a portion that is engageable with the wall bore wall surface , upon expansion thereof . the engageable surface portion has a middle band portion extending cylindrically around the outer surface , and first and second shoulder portions disposed on either side of the middle band portion . each shoulder portion extends cylindrically around the outer surface . the gripping inflatable packer also has a mechanism for gripping the wall surface of the well bore upon expansion of its bladder . this gripping mechanism includes at least one gripper device attached to the outer surface of the elastomeric bladder . the gripper device has a base plate having first and second surfaces disposed on opposite sides of the plate and at least one projecting member terminating in a point protruding from the first surface , for engagement with the well surface upon inflation of the packer .