Nonlinear internal waves are common on continental shelves and have been shown to have strong effects on acoustic propagation and scattering. Transmissions from previous field work performed in an along-shelf geometry show very strong ducting of low-frequency (50-500 Hz) sound between nonlinear waves. This strong ducting effect is acoustically important Most all of the acoustic propagation studies of internal waves have used straight line internal wave fronts for individual waves or packets. In our work, we implement a theoretical analysis using the Weinberg-Burridge horizontal rays and vertical modes formalism to study the acoustic ducting, refracting and shadowing of low-frequency sound due to curved internal waves, which seem to dominate in shelf break regions. A three-dimensional parabolic-approximation sound propagation model is also used with consideration of realistic environmental conditions, and the modeling results provide a clear depiction of the underlying physical processes. The oceanographic origin of the internal wave curvature is discussed, as this affects the predictability of the sound speed field.