Abstract The paper examines ice compression (or pressure) build-up, which may pose a threat to navigation, over various zones of the Canadian Arctic and sub-Arctic waters. The results were obtained from a multi-year program conducted at the National Research Council of Canada. The objective of that program is to quantify the risks to navigation posed by compressive ice, and to develop predictive tools to aid shipping operations in an ice environment. The work consisted of a number of activities, including: the development of an ice dynamics model tailored for high-resolution simulations of ice cover drift and deformation; creating a database of besetting events and analysis of the conditions that influence the risk of besetting; hindcasting of ice and other environmental conditions that led to besetting over various geographic regions; and the development of forecasting tools to support offshore and shipping operations and training mariners. The present paper documents the governing equations of the ice dynamics and ridging model and discusses the high-resolution implementation that makes it possible to predict the risk of vessel besetting. A case of ice compression that took place in the southern Beaufort Sea is examined. The critical values of ice pressure and ridge thickness that posed a threat to vessels during that event were found compatible with estimates corresponding to besetting events in the Gulf of St. Lawrence and Frobisher Bay.