A spatially distributed rainfall runoff model is developed with the aid of a raster GIS and minimal amount of field data that could predict the outlet hydrograph of an ungauged basin. The Basin is divided into several subareas and for each subarea a physically based advection-dispersion equation, also called diffusion wave, is used to represent the subarea response function to instantaneous excess rainfalls. The model is applied to a 173.9 km2 mountainous watershed and the calculated hydrographs are compared with the observed events and results of SCS unit hydrograph method.