A Finite Element Method (FEM) is presented to determine reflection and transmission coefficients of rectangular waveguide junction discontinuities. H-, E- plane discontinuities in a concentric/non concentric rectangular waveguide junction are analyzed using the FEM procedure. Also, reflection and transmission coefficients due to presence of a gap between two sections of a rectangular waveguide are determined using the FEM. The numerical results obtained using the FEM procedure are compared with results obtained using the Mode Matching Method (MMM) and with measured data.