In this paper, a three-dimensional analysis is presented for calculating the level ice resistance for ships that have conventional hull forms. Comparisons with published ship resistance data and other analytical predictions are also provided. The present approach combines two analytical techniques: 1) plastic limit analysis is used to describe the ice failure mechanism and the associated ice velocity field; and 2) linear and angular momentum balances determine the average ice resistance for a ship. In the momentum balance, potential flow theory is used to describe the water motion induced by the icebreaking process. Existing methods for determining ship resistance in ice include numerical methods which depend on solutions of equations of motion that describe the dynamic interaction between the ice and the ship, and empirical methods which depend on model and full-scale icebreaker data to generate empirical correlations for ship resistance. The present results compare reasonably well with published model-scale and full-scale icebreaker data. Comparisons with predictions based on other numerical methods are also discussed.