A general approach is developed for the numerical simulation of square wave voltammetry (SWV) at uniformly accessible electrodes, based on the backward implicit method. Appropriate transformations of both the spatial coordinate normal to the electrode surface and of the time variable are developed and are shown to lead to efficient and accurate simulations. The method is applied to the modeling of electrochemically reversible processes, and the results predicting the variation of peak height, width at half-height, and the area as a function of square wave frequency and amplitude are shown to be in excellent agreement with the previously derived full analytical theory. Approximate expressions for these quantities are assessed and shown to have limited value. A superior approximation is developed for the case of the peak width at half-height.