The model of Fox and Squire <1990, 1991, 1994>, which discusses the oblique propagation of surface gravity waves from the open sea into an ice sheet of constant thickness and properties, is augmented to include propagation across an abrupt transition of properties within a continuous ice sheet or across two dissimilar ice sheets that abut one another but are free to move independently. Rigidity, thickness, and/or density may change across the transition, allowing, for example, the modeling of ice-coupled waves into, across, and out of refrozen leads and polynyas, across cracks, and through coherent pressure ridges. Reflection and transmission behavior is reported for various changes in properties under both types of transition conditions. ¿ American Geophysical Union 1996