Monte Carlo calculations of deeply penetrating radiation fields are improved by use of a transformation involving the factor e-cz. The optimum value of c generally appears to be at or near the value for total attenuation coefficient for the source radiation, but there are some difficulties in choosing such a value of c. This work describes and illustrates an approach that allows c to be made equal to µo, and the resulting transformed equation is handled in a simple fashion. The technique is encoded into a FORTRAN program called FETMOC, and illustrative problems are solved. Results are given in terms of buildup factors. Two-way energy spectrum and directional distribution at arbitrary points are obtained, also. All results are compared with previously reported calculations to the extent possible.