Strong-motion displacements, recorded at 33 km (IVC) and 36 km (ELC) from the November 4, 1976 Brawley earthquake, are modeled using the Cagniard-deHoop technique. The IVC record consists almost entirely of transversely polarized motion, whereas the ELC record contains an approximately equal proportion of transversely and radially polarized motion. A simplified shear-wave velocity model was determined from the compressional wave refraction studies of Biehler, Kovach, and Allen (1964). The epicentral location and focal mechanism computed from P-wave first-arrival studies were used to locate and orient a double-couple point source within the layered half-space. The far-field time function and source depth were the only parameters without good independent constraints. A triangular far-field time function with a duration of 1.5 sec and a source depth of 7 km were sufficient to model the first 25 sec of tangential ground motion. It appears that the effects of velocity structure on the propagation of long-period SH waves are predictable in the Imperial Valley. A study of the synthetic Fourier amplitude spectra indicates that wave propagation effects should be included in studies of source spectra and seismic wave attenuation.