A computationally efficient numerical model has been developed to study the transfer of microwave radiation through a horizontally finite cloud of hydrometeors. Although drop-scattering effects are only approximated in this model, it yields radiances which agree well with more rigorous model computations. Model parameters characteristic of tropical cyclone rain cells over the ocean are specified, and the resulting microwave intensities emerging from the cloud tops at the Scanning Multichannel Microwave Radiometer (SMMR) frequencies (6.6--37 GHz) are calculated. SMMR antenna spatial response functions are estimated, based upon sensor specifications. The finite cloud model and antenna response functions serve as the basis for a rainfall rate retrieval method in which relevant model input parameters, such as the rainfall rate and rain area, are perturbed until the mean square error between model output brightness temperatures and SMMR-measured temperatures is minimized. Synthetic retrival tests indicate a significant reduction in retrieval error (50%) when information from the lower-frequency SMMR channels is added to data from the highest-resolution 37-GHz channels. Upon application of this retrieval method to SMMR imagery of three hurricanes, a mean retrieval error of 57% is achieved with respect to rainfall rates derived from digitized Weather Surveillance Radar, model 57 (WSR-57) data. ¿ American Geophysical Union 1989