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A method to compute the monostatic radar cross section (RCS) of complex bodies modeled by nonuniform rational B-spline (NURBS) surfaces is presented. The bodies can be covered by any kind of radar absorbing material (RAM) with electric and/or magnetic losses. Physical optics (PO) is used to obtain the scattered field of each surface. Fresnel coefficients are included in the stationary phase method (SPM) in order to take into account the effect of the RAM material. The contribution of diffraction by edges and double effects is also considered, improving the results of the PO approach. The diffraction is computed by the equivalent current method (ECM). A combination of geometrical optics (GO) with PO and ECM is used for the double reflection and double interaction between edges and surfaces respectively. Some simple cases are shown to validate the proposed method. The reliability of the method to analyzing the effect of covering a realistic target with RAM is also illustrated.