This paper furnishes a convenient theoretical framework for the analytical evaluation of the bistatic scattering coefficients, under the Kirchhoff approximation (KA) in electromagnetics. Starting from the KA, specific results under the geometrical optics and physical optics approximations are furnished, along with the backscattering geometry. The main aim is to provide closed-form expressions of the scattering matrix that are suited to scenarios where multiple-bounce scattering comes into play and/or surfaces with arbitrary unit normal are present. This is accomplished by addressing the following objectives: (1) to provide an explicit formulation of the scattering matrix under KA in terms of the incident and scattered unit wave vectors, (2) to provide a more generic derivation of the scattering matrix under the physical optics approximation by relaxing typical hypotheses regarding the geometry of the scattering problem, and …