The permeable element method (PEM), as the development of an arbitrary Eulerian-Lagrangian finite element approximation, intended for the description of densification of porous bodies, is elaborated. The Eulerian frame of reference, for which the material movement is independent of the movement of a discretizing network, is the basis for the consideration of the deformation process. The shape of the elements and network movement are deliberately determined from the point of view of convenience for the analysis of the calculation results. Using the PEM, the pressing of hollow cylinders in a rigid die is considered. The computed spatial density distributions are compared with the experimental data obtained, using quantitative metallography analysis. The problem of pressing an article of a stepped shape is solved. The peculiarities of material flow and density distributions are discussed.