This paper describes and analyzes a beam tracing method for computing sound propagation paths from sound sources to receivers in architectural environments. The algorithm traces polyhedral beams from the location of each sound source through a precomputed data structure encoding spatial adjacencies. The main features of the method are: 1) it enumerates all potential sequences of specular reflection, diffraction, and transmission up to user-specified termination criteria, 2) it enables evaluation of early propagation paths at interactive rates, and 3) it scales to support large, "densely-occluded" architectural environments. It is being used to support real-time auralization in immersive virtual environment applications.