During operation of transport and maneuverable gas-turbine units, there are crack formation in turbine disc rims what exerted by thermomechanical cycling loads. For in-depth study of these problems we have to use theories of plasticity and creep which form the basis for determining the complex stress-strain state in the stress concentration zone for disc rims, and a modern failure criterion which can predict lifetime under conditions of simultaneous plastic and creep strain accumulation. There is a finite-element method (FEM) that allows us to evaluate the stress-strain state in a stress concentration zone for a non-elastic material behavior. With plasticity and creep theories, it is possible to determine local strain quiet reliable by FEM.