Measurements of low-frequency sound propagation over the areas of the Australian continental shelf, where the bottom sediments consist primarily of calcarenite, have revealed that acoustic transmission losses are generally much higher than those observed over other continental shelves and remain relatively low only in a few narrow frequency bands. This paper considers this phenomenon and provides a physical interpretation in terms of normal modes in shallow water over a layered elastic seabed with a shear wave speed comparable to but lower than the water-column sound speed. A theoretical analysis and numerical modeling show that, in such environments, low attenuation of underwater sound is expected only in narrow frequency bands just above the modal critical frequencies which in turn are governed primarily by the water depth and compressional wave speed in the seabed. In addition, the effect of a thin layer of harder cap-rock overlaying less consolidated sediments is considered. Low-frequency transmission loss data collected from an offshore seismic survey in Bass Strait on the southern Australian continental shelf are analyzed and shown to be in broad agreement with the numerical predictions based on the theoretical analysis and modeling using an elastic parabolic equation solution for range-dependent bathymetry.