In several models of arc-driven rail guns, the rails are assumed to be infinitely high to simplify the calculatiOn of the electromagnetic fields in the arc. This assumption overestimates the arc pressures and accelerations by approximately a factor of two for typical rail gun geometries. In this report, we develop a simple method for modifying the infinite-height models to account for the effect of finite-height rails On the performance of the rail gun and the properties of the arc. The modification is based on an integration of the Lorentz force across the arc cross section at each axial location in the arc. Application of this technique suggests that, for typical rail gun geometries, the variation of the arc pressure (averaged over the arc cross section) can be well approximated by merely scaling the pressure profile for the case of infinite-height rails, the scaling factor being a function of the effective inductance for the finite-height geometry. Exploiting this result in a simple arc model for the Rashleight-Marshall experiment, we find that use of the finite-height model leads to considerably lower predictions for the arc pressure, density, acceleration, and arc mass when compared to the predictions of the infinite-height model for the same arc length. ON the other hand, the use of a finite-height rail gun model leads to a higher prediction for the arc muzzle voltage. A review of models which have recently been proposed for analyzing mechanical and thermal damage to the rails in arc- driven rail guns is also presented, and recommendations for future theoretical and experimental investigations of arc-driven rail guns are proposed.