A new model for the interaction of a supersonic magnetosheath flow with the high-altitude cusp is proposed. Archival and recent observations have suggested that the cusp is a region of indentation, where solar wind plasma is found earthward of the nominal magnetopause position. It is proposed that a supersonic solar wind flow interacts with such an indentation by being first accelerated through an expansion fan and then decelerated by a shock. For most realistic parameters the shock cannot originate from the deepest part of the cusp but must be detached. The rarefaction of the magnetosheath plasma leads to a rather shallow cusp (<1Re) and also implies that the cusp becomes less indented the more tailward it is located. ¿ 1999 American Geophysical Union