We develop an efficient analysis and synthesis tool for the design of transverse-mode coupled resonator filters. We describe the energy storage effect and the electrical and mechanical loading effect with a one-dimensional model. The two-dimensional nature of the problem is taken into account by shape functions, representing the nonuniform velocity, excitation, and reflection profile across the waveguide structure. We model the wave propagation, excitation, and reflection separately and use the P-matrix algorithm to piece all effects together. This approach enables us to calculate the filter transfer function with standard material data in a general way. Thus we are not restricted to a specific filter design. Our approach can be applied to all two-port devices