Two variants of indirect boundary element methods (BEM) have been proposed for solving of geometrically nonlinear problems of elasticity. These indirect BEM variants have been based on the integral representations of regular solutions of plane boundary problems. One integral representation has been a potential of a simple layer with a complex density which has been used in the imaginary load method. Another integral formula has described a potential of a double layer with a complex density for the disconnected displacement method. The techniques of calculating the stress intensity factors by means of the proposed BEM have been considered. Errors of calculating the stress intensity factors by the indirect BEM have been analyzed.