The activation energy to move a dislocation through randomly distributed solute ions was calculated as a function of applied stress, solute ion concentration and line tension of the dislocation, by using a statistical method. The interaction between a dislocation and solute ions is calculated on the basis of elasticity theory (size misfit). Critical resolved shear stress, activation volume and dislocation velocity-stress exponent were determined as a function of temperature and concentration, by assuming that the thermally activated deformation is expressed by the Arrhenius equation. The theoretical results were compared with experimental data of KC1–KBr solid solution measured from 4.2 K to 293 K and close agreement was obtained, except for a range of low concentrations at low temperatures.