Numerical simulations exploiting the time-dependent backward implicit method are used to develop the theory of square wave voltammetry as applied to electrochemically reversible processes undergoing anodic stripping at planar mercury electrodes having arbitrary film and diffusion layer thicknesses. Computations made using a time scale distorted to reflect the Cottrellian character of the transient response at short times are found to be extremely efficient when applied to this problem. For the limiting case of semi-infinite diffusion in the solution phase, excellent agreement with existing analytical theory is noted (Kounaves et al. Anal. Chem. 1987, 59, 386). The effects of the pulse frequency are investigated and, in particular, the effect of diffusion layer thickness characterized. Deviations from semi-infinite theory are predicted and rationalized for the case when the magnitude of the latter is comparable to the diffusion length of the solution-phase species during a single pulse width as might occur when measurements are made using hydrodynamic electrodes or sonotrodes.