The phase-space finite element method is applied to the multigroup neutron transport equation in cylindrical critical systems. The continuous piecewise polynomial trial functions are trilinear in the space variables and bilinear in the angle variables. Elements are triangular in the spatial domain and rectangular in the angle domain. Galerkin method is used to derive a set of simultaneous algebraic equations. The coefficient matrices of the algebraic equations are compressed and stored. The resulting finite element equations are solved by gaussion elimination method. Numerical results are compared to those obtained by SN calculations. FEM was observed to yield a higher order of convergence and accuracy.