The problem of electromagnetic (EM) scattering from an aperture backed by a rectangular cavity recessed in a three-dimensional (3-D) conducting body is analyzed using the modal expansion inside and the integral equation method outside the cavity. Assuming (1) an equivalent electric surface current density flowing on the 3-D conducting surface of the object including the cavity aperture and (2) an equivalent magnetic surface current density flowing over the aperture, only the scattered fields outside the cavity are determined . The EM fields inside the cavity are determined using the waveguide modal expansion functions. Making the total tangential electric and magnetic fields across the aperture continuous and subjecting the total tangential electric field on the outer conducting 3-D surface of the object to zero, a set of coupled integral equations is obtained. The equivalent electric and magnetic surface currents are then obtained by solving the coupled integral equation using the method of moments (MoM). The numerical results on scattering from rectangular cavities embedded in various 3-D objects are compared with the results obtained by other numerical techniques.