In papers given in previous years in this conference, a rigorous solution has been presented and experimentally verified for the 2‐D problem of an ultrasonic wave backscattered from a periodically rough surface. While predicting experiment very well, that theory has the limitation that it is very computationally intensive and that it only can be applied to the problem of planar interfaces. Practical applications, however, call for solutions that can be evaluated more rapidly and that can be generalized to the case in which the interface is curved. Such a theory is presented in this paper. The backscattering problem is formulated as a scattering process in which the strength of the scattering from individual ridges is viewed as an unknown. By summing over all scattering events and comparing to the rigorous solution, these unknown scattering strengths can be determined. In this paper, we present the theory, compare it to the rigorous solution, and use it to make numerical predictions for the effects of curvature on the backscattered noise. © 2003 American Institute of Physics