Extensions of the Sokolovsky‐Malvern theory of strain‐rate‐dependent plasticity are proposed. These extensions are based on concepts of strain‐dependent viscosity and of hereditary integral viscosity, and are based on both the linearly viscoplastic constitutive equation and on the exponentially viscoplastic one. The basic tests, creep, relaxation, and constant strain rate, are examined and the application of the theories to wave propagation is discussed.