In the work, on the basis of the determining relations between the increments of the true stresses and strains, in the framework of the finite-element discretization of the computational domain, the method of solving geometrically and physically nonlinear problems of the mechanics of a deformable solid body is implemented. A number of model problems of deforming elements of three-dimensional elastoplastic structures from solid and porous materials have been solved. It may be noted that there is a good agreement between the numerical results obtained by the proposed method and known solutions; some regularities of the deformation of structural elements made of porous materials were found.