Abstract <p>The substantiation of brittle fracture resistance and probabilistic analysis of NPP equipment and pipeline failure require the calculation of fracture mechanics parameters under multifactorial conditions of normal operation and during emergency processes. New numerical and analytical approaches to calculating stress intensity factors have been developed on the basis of the numerical solution of exact integral equations of two-dimensional elastic problems on cracks, including with analytical consideration of the perturbation of the stress state caused by the proximity of the crack front and the boundary of the body or the interface of materials. A comparison with an exact solution for one problem of fracture mechanics has been performed; the accuracy and efficiency of the proposed approaches for other problems of fracture mechanics modeling calculated cracks near the surface of equipment or pipelines or in the area of the interface between the base metal and the weld deposit have been demonstrated.</p>