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A method of computing resonance absorption by a rod in a two-region cylindricalized cell that is not based on the assumption of an symptotic neutron source distribution is developed and used to write a FORTRAN program RIFF RAFF (RP 359X), for the CDC-3600. An energy range of interest is divided into extremely narrow intervals of equal lethargy width. For each interval, the source distribution in each region is taken to be a three-term polynomial. By using this form for the source and the assumption that neutrons enter the rod isotropically, the reaction rates and the flux distribution for the interval are obtained. The reaction rates are accumulated over specified energy intervals to obtain resonance integrals; the flux distribution is used to obtain the source distribution for intervals at lower energies.