In solving photon transport problems by the Monte Carlo method, parallel-type computers are not well suited to the use of the customary rejection technique for selecting photon wavelength upon scattering. Two techniques of determined length and therefore greater suitability have been studied, with particular application to a machine having 64 processing elements, such as ILLIAC IV. The method involving solutions by Newton’s method of the exact equation derived from the Klein-Nishina formula is found to be still more time-consuming than the rejection technique on both sequential and parallel computers. However, newly devised approximation formulas, corrected by weight adjustment factors, have been found to be much quicker on a parallel computer than the rejection technique, and even competitive on a sequential computer.