A program for simulating ice accretion on an offshore structure due to spray generation from wavestructure impacts is presented in this paper. The program is an upgraded version of RIGICE that was first developed in 1987 and incorporates a number of improvements, specifically: a more accurate expression for the equilibrium freezing point of seawater, an empirical expression for sponginess of marine ice as a function of air temperature, a spray liquid water content versus height model that is matched with field data, and a new algorithm for estimating the frequency of significant spray events that generate spray clouds above 10 m high. Comparisons of ice accretion predictions are presented between the current version, RIGICE04 and a previous version, N_RIGICE. Generally, RIGICE04 predicts lower total ice accretion mass than N_RIGICE. RIGICE04 results are also compared with measured ice accretion duration on an offshore rig operating on the East coast of Canada. The current prediction is in good agreement with the measured duration; while the N_RIGICE prediction was more than twice the measured duration. RIGICE04 is more accurate than N_RIGICE although more comparisons with field data are required.