Among the methods for determining the parameters of fracture mechanics on the basis of FEM the most widely used energy approaches. To date, numerous studies have been carried out to demonstrate the effectiveness of the reaction method in implementing the energy approach. However, in these studies, the question of determining the J-integral is considered. It is generally known that in the presence of bulk forces of different gauge, the J-integral can not be used to assess the crack resistance. Therefore, in this paper, a generalization of the reaction method is carried out to determine the Griffiths criterion, which allows us to assess the crack resistance under the influence of bulk forces of different nature. In determining the work of external forces and the potential energy of deformation are determined by known formulas in terms of displacement. For this purpose, in discrete models, a spatial body with a crack in two equilibrium states is considered. The first state corresponds to the initial position of the crack, the second to the new position obtained with the growth of the crack for one step of the grid with the emergence of a new surface of the crack. Existing methods for calculating G in discrete models allocate a certain region around the crack front. Therefore, by analogy, the definition formula for a closed volume around a crack of arbitrary configuration was derived. With the invariance of the stiffness matrix of the volume fragment in both states under consideration, the definition formula acquires a simplified form. Approbation of the developed technique was carried out on the test problem of stretching an infinite plate with a central crack. The calculation was carried out both in the entire discrete model and in a closed volume of different dimensions, covering the peak of the crack. The obtained results of calculating the parameter in the complementary region and for the entire discrete model coincide. Moreover, this property is preserved both in surface and volumetric forces. Next, the scheme of application of the developed method for determining the parameter for three-dimensional problems based on the semi-analytic method of finite elements was considered. To test the scheme, a test task was performed on the definition of G in a prismatic body with a lateral incision loaded with load distributed along the face. Distribution G, obtained with the use of three-dimensional FEM and SFEM, coincides with the results obtained by other methods.