In this paper, we describe a three-dimensional baroclinic sea model and its application to the computation of the internal tide over a shelf and shelf edge region. The model covers the Malin-Hebrides shelf and shelf edge with water depths ranging from a few meters near shore to over 2000 m in the deep sea. A fine horizontal grid resolution of 1/24¿¿1/24¿ (about 2.4 km east-west and 4.6 km north-south grid spacing) and 50 vertical computational levels enables us to examine the internal tide generation at the shelf edge and its propagation. Numerical calculations illustrate the generation of the internal tide over the shelf edge and its propagation toward both the shelf and deep sea in a strongly stratified surface layer (the case of summer stratification). In a weakly stratified surface layer case (winter stratification), the internal tides generated at the shelf edge are much weaker and are dissipated away from the shelf edge region, in particular over the shallow shelf because of strong tidal mixing. A comparison of observed and computed tidal currents is made under a range of stratified conditions, and this shows the difficulty in rigorously validating three-dimensional internal tidal models. The model also indicates that the Anton Dohrn and Hebrides Terrace seamounts have an important influence upon the internal tide propagation in the region. ¿ 1998 American Geophysical Union