A study has been made at Atomics International to find and apply improved numerical methods for solving the gamma-ray transport problem in multidimensional structures. It appears that such problems can be solved systematically, economically and with acceptable accuracy by using the variational synthesis method. This method provides the means for obtaining approximate solutions for problems in multidimensional structures by joining togehter solutions of similar problems of lesser dimensionality and/or guesses for solutions based on intution or past experience.