The problem of mathematical simulation of the origin and evolution of low-cycle fatigue cracks is quite actually for many high-loaded machines and units of power industry, aerospace engines, oil and gas pipelines and other structures operating under repeated loading. Successful prediction of low-cycle resource depends on solution of several interrelated problems: creation and development of structure model (loads, boundary conditions, materials model) that will adequately describe all aspects stress-strain history in the structures paths; creation plasticity and creep models adequate to the processes taking place during sing-alternating elastic-plastic deformation; the creation of lifetime fatigue failure rate criteria; and development of effective numerical simulation technique.