This paper describes an electromagnetic computer prediction code for generating radar cross section (RCS), time domain signatures, and synthetic aperture radar (SAR) images of realistic 3-D vehicles. The vehicle, typically an airplane or a ground vehicle, is represented by a computer-aided design (CAD) file with triangular facets, curved surfaces, or solid geometries. The computer code, XPATCH, based on the shooting and bouncing ray technique, is used to calculate the polarimetric radar return from the vehicles represented by these different CAD files. XPATCH computes the first-bounce physical optics plus the physical theory of diffraction contributions and the multi-bounce ray contributions for complex vehicles with materials. It has been found that the multi-bounce contributions are crucial for many aspect angles of all classes of vehicles. Without the multi-bounce calculations, the radar return is typically 10 to 15 dB too low. Examples of predicted range profiles, SAR imagery, and radar cross sections (RCS) for several different geometries are compared with measured data to demonstrate the quality of the predictions. The comparisons are from the UHF through the Ka frequency ranges. Recent enhancements to XPATCH for MMW applications and target Doppler predictions are also presented.