Edge waves on ice-covered water, generated elsewhere by wind, current, or wave impingement at the ice edge, can reach large amplitudes where bottom slope and current combine to give low group velocity. The amplitude of water velocity normal to shore can become large, and the resulting acceleration of the ice cover onto shore may be sufficient to cause ice rideup. Edge waves on an ice-covered ocean with a mean current are analyzed to linear approximation, and estimates are given of velocities and amplitudes.