A fully three‐dimensional model for the motion and bending of a solitary ice floe due to wave forcing is presented. This allows the scattering and wave‐ induced force for a realistic ice floe to be calculated. These are required to model wave scattering and wave‐induced ice drift in the marginal ice zone. The ice floe is modeled as a thin plate, and its motion is expanded in the thin plate modes of vibration. The modes are substituted into the integral equation for the water. This gives a linear system of equations for the coefficients used to expand the ice floe motion. Solutions are presented for the ice floe displacement, the scattered energy, and the time‐averaged force for a range of ice floe geometries and wave periods. It is found that ice floe stiffness is the most important factor in determining ice floe motion, scattering, and force. However, above a critical value of stiffness the floe geometry also influences the scattering an