Abstract: Recently, a new technique refered to as the on-surface radiation boundary condition (OSRC) approach was presented to calculatc the electromagnetic scattering by con-vex structures. When the scatterer is with first-order surface discontinuities, the OSRC obtained by this new technique is very inaccurate. Thus there are many limitations about the application of the OSRC approach. In this paper, the OSRC approach is modified, and a method to deal with the scattering by convex two-dimensional objects with arbitrary singular edges is presented. This method is applied to calculate monostatic and bistatic rader cros-section from convex scatterers with nonsmooth surfaces. The result shows that OSRC approach greatly improves the accuracy of the scattered field prediction .