We present an investigation of the effect of magnetic overshoot (a feature of supercritical, collisionless shocks) on the shock drift acceleration (SDA) mechanism. The investigation is carried out by performing numerical simulations of ensembles of test particles (ions) to obtain reflection probabilities, energy gains, and anisotropies. We assume that the test particle approach is valid since the lowest-energy particles studied have speeds several times the ion thermal speed in the upstream plasma frame, which corresponds to a very small percentage of the overall population. We show that the magnetic overhsoot enhances particle reflection considerably when the initial gyroradius of the particle is of the order of the shock transition length. Furthermore, as compared to the no-overshoot case, the overshoot allows initially lower energy particles to reflect. This in turn, gives rise to more field-aligned beams upstream of the shock. The test particle results display adiabatic-like characteristics and indicate that the structures shock may be analytically modeled by an energy-dependent magnetic mirror. The results presented here are in agreement with a similar study in which the electromagnetic fields were provided by a self-consistent hybrid simulation. This investigtion has applications to the regions of the outer planetary bow shocks, where curvature effects are considerably smaller than at the Earth's and at strong interplanetary shocks ≲1 A.U., where the overshoot may still be significant. ¿1991 American Geophysical Union