Problems of reliable functioning and materials consumption decrease for modern technique constructions operating under conditions of high level of power and temperature loadings, and ionizing radiation is problematic in the mathematical modelling of nonelastic behaviour. The increase in working parameters of modern machines and devices leads to an increase in both the general and local intensity of construction. Real loading processes for such constructions lead to nonelastic (viscous-plastic) deformations. Thus the loading is a complex nonisothermal one, and a mode of its changes may be repeated and continuous influence of the thermal power loadings and ionizing radiation. Theories of plasticity, creep and nonelasticity based on the nonisothermal loading now-in-use lead to the authentic results under narrow limited conditions when loadings are close to ordinary and stationary. Separated examination of processes of plasticity, creep and damage accumulation without considering their mutual influence is proper to all theories applied in calculations. Such prominent aspects influencing damage accumulation as brittle behaviour and healing are not considered practically. The theory of nonelasticity belongs to the class of single-surface theories of flow under the combined loading. Comparisons of calculations under various theories of plasticity, creep and nonelasticity have shown that the results received by the means of the developed theory of nonelasticity best correspond to the experimental data. On the basis of this research, the developed theory of nonelasticity can be applied to practical calculations of nonelastic behaviour and material damage accumulation of construction material under unrestricted process of complex nonisothermal loading. An authentic forecast for lifetime of high rating construction material under repeated and continuous influence of the thermal power loadings and ionizing radiation can be made on the basis of this theory. The range of applications of the theory of nonelasticity is limited by a small strain of homogeneous and initially isotropic metals at temperatures when there is no phase transformation, and deformation rates when dynamic effects can be neglected.