**Abstract**

At the solution of integrated tasks of strength, safe life and service safety maintenance for the nuclear power plants (NPP) equipment with slow reactors—watermoderated power reactors (WMPR) of VVER type and channel-type graphitemoderated power reactors (GMPR) of RBMK type arise necessity of physical and mathematical modeling of nonlinear processes of a deformation, fracture and damage at nonlinear probability statement. First of all, it concerns deriving determined, statistical and probabilistic characteristics of mechanical properties of reactor materials. Expectations and variation factors of mechanical properties' characteristics obtained from experimental researches are inducted into the equations for the verification calculations at determination of static and cyclic strength margins with the use of nominal and local stresses and strains. For the improved determined and probability analysis of these margins modeling experimental researches of stress-strain states of the analyzed equipment are conducted. Special attention at such tests is given to concentration factors and variation factors of loading conditions. The final stage of estimation of basic normative and verification calculation accuracy at laboratory, modeling and test bench researches are full-scale pre-operational tests (cold-hot running-in) of pilot nuclear reactors with the use of the experimental mechanics methods. The conditions of safety service of the NPP equipment are estimated taking into account factors of reaching limiting states by criteria of risk of initiation of emergency situations.

**Keywords:** probability modeling, strength, deformation, damages, fracture, nuclear reactors, safety service, risk, structural materials
