This paper presents a new three-dimensional propagation model for microcellular communications in an urban street scene. The model is based on the Uniform Theory of Diffraction and takes into account multiple reflections between wall-to-wall, wad-to-ground, and ground-to-wall as well as the diffraction from corners of buildings, and also subsequent reflections from such diffracted signals. The ray geometry is made extremely complex by the presence of ground reflections, and the many combinations of sequences of reflections or diffractions from walls, edges, and ground. The major difficulty in this three-dimensional formulation lies in determining the exact point of reflection at a surface, or exact point of diffraction at an edge, and the corresponding plane of incidence. This is necessary to enable us to calculate the polarization components of the reflected or diffracted rays and their subsequent trajectories. At each reflection or diffraction point, use is made of the local ray-fixed coordinate system or edge-fixed coordinate system together with appropriate dyadic reflection or diffraction coefficient matrices. Our theoretical results of the signal path loss along the streets are compared with measurements done in New York and Tokyo for various values of the propagation parameters. The good agreement with these measurements indicates that our UTD formulation is a good model for such urban communication applications.