The time-dependent transport equation in plane geometry has been solved numerically using the double spherical harmonics angular approximation and first-order finite differences. The monoenergetic case has been shown to meet both necessary and sufficient conditions for stability for reasonable values of the time step. The convergence and wave front propagation characteristics of the difference scheme have also been checked in special cases and found to be satisfactory. A computer program has been written to solve the difference equations of the multienergy, multiregion problem. Monoenergetic and multigroup calculations have been made which compare qualitatively with experimental results.