A theory of the flow stress of metal crystals with high concentrations of solute atoms is developed with the help of the theory of stationary random functions. The dislocation model used to calculate the critical flow stress is a Frank‐Read source. Under the assumption that at high concentrations of solute atoms the dislocation will interact principally with groups of atoms spread out along the dislocation line rather than with single atoms, no thermal activation can take place. This results in a temperature‐independent critical flow stress, which is indeed observed in solid‐solution crystals as the so‐called plateau stress. The theory requires that the plateau stress increase with solute concentration proportional to [C(1−C)]1/2and, at fixed concentrations, be proportional to the magnitude of the interaction between solute atoms and dislocation.