A set of finite-difference equations which approximate the plane-strain motion of a rotatory inertia and transverse shear plate are examined in detail. The equations are stated in such a form that the usual norm is an energy expression. Proper posedness, consistency, stability, and convergence are all examined. The von Neumann stability analysis is supplemented by a numerical verification. The critical time step size is shown to fall into three different regimes depending on the ratio of mesh size to plate thickness. The largest allowable time step size is found to be dictated not by mesh spacing, but rather by physical dimensions of the plate.