[en] The application of the finite element method in the solution of multigroup diffusion equations of a nuclear reactor is described. The problem is solved for a cylindrical reactor which is divided into subregions, each subregion having different material properties. The non-self-adjoint eigenvalue problem is converted by the source iteration method to a sequence of inhomogeneous boundary value problems with sources; these problems are solved by the finite element method using symmetry properties. Attention is paid to a proof of applicability of the finite element method in the cylindrical geometry, and also to the transmission problem. The convergence of the power iterations and finite element methods in combination is proved. Some numerical results for a cylindrical five-zone reactor in the 6-group approximation are given. (author)