Computational and analytical methods have been used in a study of particle acceleration by MHD shocks. Numerical simulations of single-particle trajectories indicate that magnetic moment is conserved quite accurately for an encounter with a near-perpendicular shock, and for all pitch angles except the very small ones. Acceleration is most effective for particles which are reflected by the shock at small pitch angles. If future encounters with the shock are possible, large acceleration will be repeated only for relativistic plasma flow velocities. Results for the pure MHD shock are then considered within the context of a diffusion model (hence a diffusive MHD shock). The microscopic approach is employed whereby one follows the history of a test particle and explicitly takes into account the possibility of reflection by the shock. Exact analytical solutions are currently available to order V/c, where V is the plasma flow speed, and are found to be in complete agreement with diffusion theory. More specifically, the presence of electromagnetic effects leads to a shortening of acceleration time scale but does not change the steady state spectrum of energetic particles. 7 refs.