Solid solution strengthening increases yield strength of the material by increasing the shear stress, , to move dislocations:
where c is the concentration of the solute atoms, G is the shear modulus, b is the magnitude of the Burger's vector, and  is the lattice strain due to the solute. This is composed of two terms, one describing lattice distortion and the other local modulus change.
Here,  the term that captures the local modulus change,  a constant dependent on the solute atoms and  is the lattice distortion term.
The lattice distortion term can be described as:
, where a is the lattice parameter of the material.
Meanwhile, the local modulus change is captured in the following expression:
, where G is shear modulus of the solute material.