Experimental measurements of fission product capture cross sections and statistical estimates of capture cross sections for energies at which no measurements have been made have yielded a set of group cross sections for primary and secondary fission products covering the complete range of energies of interest for reactor calculations. Capture cross sections and fission product yield measurements have been obtained from a comprehensive search covering published and some unpublished measurements available prior to May 1961. Unmeasured capture cross sections in the resonance region have been statistically estimated using average neutron strength functions, level spacings, and radiation widths. The general techniques of obtaining reliable nuclear parameters and estimates of cross sections are discussed in detail. The importance of capture in short-lived fission products is considered. The group cross sections obtained in this work have been combined and presented in a form useful for calculating fission product poisoning in reactors containing U233, U235, and/or Pu239. Results are analyzed and compared with previously published fission product studies.