Abstract The extension of a variational finite-element method of solving the neutron transport equation, to include multigroup-energy dependence in R- Z geometry, is evaluated. The method is implemented in a computer program called felicit. The solutions obtained by means of felicit to a number of axisymmetric test problems are given in numerous tables and graphs. A comparison is made between felicit, exact solutions and solutions obtained by other transport techniques. The ability of the method to handle problems characterized by difficult geometries is demonstrated; in particular by considering a fixed-source problem in a model Tokamak configuration.