The present paper treats the motions of an ice mass up to the instant of impact with a large fixed offshore structure, and describes a numerical method for predicting these motions taking account of the interaction between the ice mass and structure. In general an ice mass will undergo wave-induced oscillatory motions as well as drift motion. The former are calculated by linear diffraction theory applied to bodies of arbitrary shape so that interaction effects are fully accounted for. The drift motion is calculated by a time-stepping procedure applied to the drift equations of motion which involve zero frequency added masses, drag forces and wave drift forces. As an example of the methods application, results are presented for a typical design situation which illustrate the nature of the hydrodynamic interaction between the ice mass and structure.