The book provides basic ideas about the finite element method (FEM) and how to implement it in problems of linear and nonlinear fracture mechanics. Its content covers a wide range of issues - from methods for calculating stress intensity coefficients in flat and axisymmetric bodies during mechanical and thermal loading of plastically deformed areas and local destruction parameters in the case of a developed plastic zone and to a number of computational experiments that help solve complex issues of mechanical behavior of elastic-plastic bodies with cracks.