The magnetohydrodynamic excitation of a cold magnetized plasma in a cavity by externally imposed pressure perturbations is examined through use of various simple models. The purpose is to outline the possible responses triggered in the terrestrial magnetosphere by the changes in the solar wind dynamic pressure or other sources of pressure perturbation at the magnetopause. Although the source is compressional, the impulse response of a uniform plasma in a cavity is found to contain both fast and transverse mode oscillations. When nonuniformity is introduced in the model, the fast and transverse signals couple and field line resonances and damped global eigenmodes appear in the response. Field aligned currents are a necessary component of any ionospheric response to compressional perturbations but arise only in models that allow for the nonuniformity of the system. The field-aligned currents drive ionospheric motions similar to those predicted as signatures of flux transfer events on the magnetopause. The models qualitatively fit with the recent space, ground-based and ionospheric radar measurements of magnetospheric response to solar wind changes. ¿ American Geophysical Union 1990