A metallic strip on a dielectric substrate placed in the E-plane of a rectangular waveguide is used to make millimetric wave bandpass filters. In this paper the least squares boundary residual method (LSBRM) is employed for the mode matching technique to analyze and determine the equivalent circuit of an E-plane metallic strip on a substrate. In this method, an error function is constructed using the Eand H-field boundary conditions over the interfaces between various waveguide sections. The minimization of the error jmction determines the amplitudes of the excited modes. The weighting factors, which multiply various terms of the error fiLnction. provide some flexibility for the proposed method. n e results obtained by LSBRM compare well with those available in the literature.