In order to achieve noticeable material strengthening via solution strengthening, one should alloy with solutes of higher shear modulus, hence increasing the local shear modulus in the material. In addition, one should alloy with elements of different equilibrium lattice constants. The greater the difference in lattice parameter, the higher the local stress fields introduced by alloying. 
Alloying with elements of higher shear modulus or of very different lattice parameters will increase the stiffness and introduce local stress fields respectively. In either case, the dislocation propagation will be hindered at these sites, impeding plasticity and increasing yield strength proportionally with solute concentration. 
Solid solution strengthening depends on:
* Concentration of solute atoms
* Shear modulus of solute atoms
* Size of solute atoms
* Valency of solute atoms (for ionic materials)
For many common alloys, rough experimental fits can be found for the addition in strengthening provided in the form of:
where  is a solid solution strengthening coefficient and  is the concentration of solute in atomic fractions.
Nevertheless, one should not add so much solute as to precipitate a new phase. This occurs if the concentration of the solute reaches a certain critical point given by the binary system phase diagram. This critical concentration therefore puts a limit to the amount of solid solution strengthening that can be achieved with a given material.