Concept of shifted frequency internal equivalence (SFIE) for electromagnetic scattering problems involving homogeneous or inhomogeneous bodies is explained and applied to multi-frequency electromagnetic scattering from inhomogeneous dielectric and/or magnetic rectangular waveguides. As is well known, surface integral formulation is only applicable to homogeneous structures, and in volume integral formulation it is necessary to repeat the solution process by generating data at each incident field frequency.Here, it is shown that, volume interaction part of the data generated only at a single frequency may be utilized at other frequencies in a wide frequency band while applying SFIE. Upon combination with an external equivalence, the solution is readily obtained.