The problem of electromagnetic scattering by capacitive discontinuities located in rectangular waveguides, in particular when dealing with discontinuous conductors of finite thickness, is analyzed using the modified residue-calculus method, and form of the equation suitable for a numerical calculation is derived. The incident wave is taken to be the dominant mode, and reflection and transmission properties of an asymmetric capacitive iris are discussed. After the modal representation of the filed, the modal matching is apply to satisfy the boundary conditions at the discontinuity. And using the modified residue-calculus method, simultaneous infinite equations, which are concerned with the scattered mode coefficients, are derived. Then they are approximated at the thick diaphragm. The solutions obtained take on the form of an infinite product, and a numerical solution based on the method of successive approximations is presented as a technique for concretely determining the reflection coefficients. As confirmation, experiments are also carried out in the X-band and close agreement is shown between the calculated and experimental values.