A rigorous method for representing the multilevel cross sections and its practical applications are described. It is a generalization of the rationale suggested by de Saussure and Perez for the s-wave resonances. The rationale can be interpreted as the natural consequences of the important physical condition that the collision matrices must be single valued and meromorphic in momentum space. Thus, the latter can be rigorously represented by rational functions with simple poles in √E domain for all states. Such representation is especially attractive when it is used in conjunction with the applications of the R-matrix parameters and the subsequent Doppler broadening using Solbrig’s kernel. A computer code WHOPPER has been developed to convert the Reich-Moore parameters into the pole and residue parameters in momentum space. Sample calculations have been carried out to illustrate that the proposed method preserves the rigor of the Reich-Moore cross sections exactly. An analytical method has been developed to evaluate the pertinent Doppler-broadened line shape functions. Since the principal parts of these functions are identical to the widely used ψ and χ functions when applied to the energy region above 1 eV, the method is readily amenable to many existing processing codes. A discussion is presented on how to minimize the number of pole parameters so that the existing reactor codes can be best utilized.