In this paper, waveguide banpass filters using H-plane step discontinuities are designed based on the field theory analysis and optimization of the resonator lengths as well as dimensions of discontinuities, instead of the conventional synthesis method based on the equivalent circuit. The waveguide inductive obstacles introduced by H-plane step discontinuities analyzed using mode-matching method and the generalized scattering parameters are derived. Using the derived scattering parameters of the discontinuities as well as those of resonators, waveguide bandpass filters are designed through optimization method, modified Razor search method proposed by J.H.Bandler. Using this design procedures, waveguide bandpass filters are designed and tested at X-band(center frequency 10GHz) as well as Ka-band(center frequency 35GHz).