A computer-based method for treating the motion of charged and neutral particles called the phase space time evolution (PSTE) method has been developed. This technique, instead of utilizing the integrodifferential transport equation and solving it by computer methods, makes direct use of the computer by employing its bookkeeping capacity to literally keep track of the time development of a phase space distribution of particles. This method is applied in this paper to a study of electron transport. In this application use is made of the continuous slowing down approximation for energy degradation and the Goudsmit-Saunderson distribution for multiple scattering. The specific problem investigated considers a 1-MeV beam of electrons normally incident on a semi-infinite slab of aluminum. Results of the PSTE calculation for this problem are compared with existing Monte Carlo calculations and experimental results on the basis of number transmission, energy spectrum, and angular distribution as a function of penetration. The general agreement exhibited is good. In addition to the above, time-dependent PSTE electron penetration results for the same problem are presented. The computer time required to make the PSTE calculation discussed here was ≈ 10 min on the CDC-6600 computer at Brookhaven National Laboratory. Noteworthy is that during this small amount of machine time, the PSTE method generates both deterministic and time-dependent results.