Numerical formulations and programming algorithms are given for the THREETRAN computer program which solves the discrete ordinates, multigroup transport equation in (x,y,z) geometry. An efficient, flexible, and general data-handling strategy is derived to make use of three hierarchies of storage: small core memory, large core memory, and disk file. Data management, input instructions, and sample problem output are described. A six-group, S/sub 4/, 18 502 mesh point, 2 800 zone, k/sub eff/ calculation of the ZPPR-4 critical assembly required 144 min of CDC-7600 time to execute to a convergence tolerance of 5 x 10/sup -4/ and gave results in good qualitative agreement with experiment and other calculations. 6 references