The process of swaging using four flat anvils and simple translational feeding, has been numerically analysed by means of the Finite Element Method (FEM). Application of 3D elements, requiring substantial computing time, is necessary in the FEM analysis due to the kinematics of the tools' movement and of the deformed metal and due to the nature of the metal flow in the deformation gap. An attempt has been made to solve the problem of simulation of the stress state and of analysis of the flow scheme in the swaging process using an FEM solution for plane 2D elements and introducing assumptions enabling conversion to to a 3D solution. The assumptions presented lead to an original method of solving the problem of modelling the swaging process and permits a 3D analysis of the behaviour in the deformation gap by considering flat sections occupying consecutive positions between the entrance and exit planes of the analysed deformation gap. The assumptions taken in the model have been verified experimentally. The results of the calculations obtained have been compared with the results of trial forgings produced under industrial operating conditions. The temperature distributions on the band section obtained have also been verified by comparison with pyrometric temperature measurements on the surface of the bars.