The article proposes a statistical theory of inelasticity of endochronic type, which takes into ac- count initial microstresses and initial microdeformations, that are contained in the material. The theory main relations are formulated. The examples of the two-and one-element models were taken Известия МГТУ «МАМИ» No 1(19), 2014, т. 4 7 Аннотации статей. to provide calculations of hypothetical material uniaxial loading, which demonstrate the approach by assuming a uniform distribution of initial microdeformations. There is emphasized that in the process of loading the structural elements of the model can generate deformation of different signs that expands the boundaries of applicability of the theory.