The paper considers a load moving with a constant velocity across an ice sheet that is floating on water. The ice sheet is assumed to be an isotropic, elastic, thin plate extending to infinity. The water is assumed to be inviscous, incompressible, and of a constant depth. The dynamic equations describing this ice-water system are solved for the steady state solution. Both a concentrated load and a uniform load distributed over a circular area are considered. The velocity which causes resonance is determined. The deflection and stress directly under the load are numerically evaluated.