The magnetopause is in continuous motion and shock waves and impulsive acceleration events can occur. In fluid dynamics, when a shock wave encounters a fluid discontinuity, the interface may become unstable and form bubbles and spikes. We consider this Richtmyer-Meshkov instability in magnetohydrodynamics through a set of numerical calculations for the magnetopause configurations. We suggest that the instability may be a mechanism for generating transient events in the magnetosphere. At the dayside magnetopause, the instability tends to be stabilized by the magnetic field. Instead, the shock wave interaction can initiate magnetic field reconnection for the southward IMF, which may connect with the onset of substorms. ¿ 2000 American Geophysical Union