We apply a two-dimensional, nonlinear hydromagnetic computer code to the problem of pure fast mode cavity resonances in a box model of the magnetosphere. The cavity modes are excited by a magnetopause compression and relaxation with maximum boundary velocity v0. The results show that significant mass transport of relatively low energy plasma by the wave fields may be possible for v0/A0~0.2, where A0 is the Alfv¿n speed at the boundary. For a likely field-aligned perturbation structure, the mass tends to accumulate at and near the equatorial plane. We interpret this mass transport as being driven by the ponderomotive force, which is finally limited by opposing pressure gradients in a finite &bgr; plasma. Heating by adiabatic compression of the plasma is also seen. ¿ American Geophysical Union 1990