Extreme sea levels associated with severe cyclonic storms are common occurrences along the east coast of India. The coastal districts of Orissa have experienced major surges in the past. The recent Paradip super cyclone is one of the most severe cyclones, causing extensive damage to property and loss of lives. Extreme sea levels are major causes for coastal flooding in this region. Damages can be minimized if the extreme sea levels are forecast well in advance. In the present study, we develop a location specific, fine resolution model for the Orissa coast on the lines similar to that of IIT-D storm surge model (Dube et al. 1994). The model runs on a personal computer. The bathymetry for the model is extracted from very fine resolution naval hydrographic charts for the region extending from the south of Orissa to south of West Bengal. A simple drying scheme has also been included in the model in order to avoid the exposure of land near the coast due to strong negative sea surface elevations. An attempt was made in this study to simulate extreme sea levels along the Orissa coast using the data of past severe cyclones. The model results reported in the present study are in good agreement with available observations or estimates.