The finite element method is applied in multigroup formalism to the analysis of some fast and intermediate spherical critical systems. The approximation scheme is based on a self-adjoint variational principle associated with the formally self-adjoint form of the monoenergetic transport equation. A number of experimental critical assemblies are analyzed using unmodified and modified Hansen-Roach 16-group cross sections. Comparison of the results with those obtained by SN calculations indicates that high accuracy is obtained by low-order finite element techniques. Several optional strategies are proposed which may further accelerate the convergence of finite element solutions.