The finite element method is applied to the one-dimensional neutron transport equation. Piecewise bilinear or trilinear polynomials that are continuous in the space-angle phase space are utilized in an even-parity functional for the angular flux to establish linear simultaneous sets of algebraic equations. Both inhomo-geneous and eigenvalue problems in slab, spherical, and cylindrical geometries are treated. The application of the finite element method to problems with anisotropic scattering and material interfaces is also demonstrated. In all cases, the accuracy of the finite element results is an improvement over that obtained from standard SN calculations using comparable numbers of simultaneous equations.