The South Caspian Basin contains one of the thickest sedimentary deposits in the world. Intermediate-frequency (0.02–0.04 Hz) fundamental-mode Rayleigh waves propagating across the basin are severely attenuated, but apparent attenuation is significantly less for both low and high frequencies. We have modeled the response of surface waves in a simplified rendition of the South Caspian Basin model of Mangino and Priestley (1998) using a hybrid normal-mode/2D finite-difference approach. To gain insight into the features of the basin that cause the anomalous surface-wave propagation, we have varied parameters of the basin model and computed synthetic record sections to compare with the observed seismograms. We have varied the Moho depth beneath the basin, the shape of the basin boundaries, the thickness and shear-wave Q of the sediments and mantle, and the water depth. Of these parameters, the intermediate-frequency surface waves are most severely affected by the sediment thickness and shear-wave attenuation. All models fail to satisfy observations for frequencies of 0.05 Hz and above, and this failure is attributed to significant 3D wave propagation effects caused by focusing and scattering of surface waves by basin structures.