Coastal flooding in developed areas can be catastrophic. As an essential element in coastal water level prediction, a two-dimensional numerical model of long period wave behavior is presented. The time dependency is treated implicitly for cost-effective simulation of coastal flooding from hurricane surges or other hydrodynamic phenomena such as extratropical storm surges, tides, tsunamis, etc. An important feature of the model is use of a coordinate transformation in the form of a piecewise exponential stretch. Such a technique permits simulation of a complex landscape by locally increasing grid resolution and/or aligning coordinates along physical boundaries. The model is applied to Galveston Bay, Texas, for storm surge and coastal flooding from Hurricane Carla 1961. Verification for the Galveston area was accomplished by using physical model data from simulations of free gravity waves (tide and design surge). Subsequent hindcasting of Carla produced good agreement between observed and computed surges with a mean absolute error of 0.18 m for peak elevations.