This dissertation presents three different aspects of the incorporation of directionality into the Monte Carlo ray-trace (MCRT) environment: (1) the development of a methodology for using directional surface optical data, (2) the measurement of the bi-directional reflectivity functions for two different surfaces, and (3) MCRT simulations performed using these directional data sets. The methodology presented is based upon a rigorous analytical formulation and is capable of performing simulations of radiation exchange involving directional emission, absorption and reflection given the bi-directional reflectivity functions (BDRF) of the participating surfaces. A wavelet compression technique is presented for the management of extremely large directional data sets. The BDRFs of two different surfaces were acquired using a Surface Optics Corporation model SOC-250 bi-directional reflectometer. These data were processed according to the methodology presented and an MCRT code was used to simulate the action of the SOC-250 in measuring radiant energy reflected from the surfaces of the two samples when illuminated by the source of the SOC-250. Another MCRT code was used to simulate the radiant energy reflected into a plane at the exit of an open-ended rectangular box when the entrance to the box is illuminated by source of the SOC-250. The RMS error between the MCRT simulations of sampling using the SOC-250 and the measured data were determined and then divided by the mean BDRF level of the measured data (RMS/mean[rho]) to provide an estimate of convergence. The RMS/mean[rho] was observed to fall from as much as 138 to 0.84 for the aluminum substrate coated with Krylon Shortcuts Hunter Green Satin aerosol paint as the number of energy bundles emitted in the MCRT simulation went from 103 to 106 at an incident zenith angle of 40 deg. The RMS/mean[rho] was observed to fall from as much as 2.2 to 0.2 for the Norton (150 Fine grit) all-purpose sandpaper coated with Krylon Shortcuts Hunter Green Satin aerosol paint as the number of energy bundles emitted in the MCRT simulation went from 103 to 106 at an incident zenith angle of 40 deg. / Ph. D.