A large ion temperature anisotropy (Ti⊥/Ti∥≂2--3), which may lead to the generation of mirror waves, is found to exist downstream of a quasi-perpendicular shock simulated by a one-dimensional hybrid code. In the case of the Earth's bow shock, large amplitude (ΔB~B0) mirror waves are found to develop approximately 0.5--1 RE (Earth radius) downstream of the shock ramp. It is found that the instability criterion for mirror waves in the downstream region is satisfied for shocks with a large Alfv¿n Mach number (MA>3). ¿ American Geophysical Union 1988