During the onset of coronal mass ejections, a front of enhanced EUV emission is sometimes seen to propagate away from a flaring active region across the solar disk. We present model simulations to test the hypothesis that these transients (called "EIT waves") represent fast-mode MHD waves. The distribution of the magnetosonic velocity vf in the corona is determined using a current-free extrapolation of the measured photospheric field and a density scaling law for coronal loops. In agreement with observations, the waves are deflected away from active regions and coronal holes, where vf is large; they are also refracted upward as they propagate away from their initiation point, since vf falls off rapidly above active regions. The average surface-projected expansion speeds are only of order 200 km s-1, comparable to or somewhat smaller than those of EIT waves observed during 1997-1998. The model is unable to account for the velocities in excess of 600 km s-1 associated with Moreton waves and type II radio bursts unless it is assumed that the initial disturbance has the form of a strong, super-Alfvénic shock.