In this work, the radiation environment on the Martian surface, as produced by galactic cosmic radiation incident on the atmosphere, is modeled using the Monte Carlo radiation transport code, High Energy Transport Code-Human Exploration and Development in Space (HETC-HEDS). This work is performed in participation of the 2016 Mars Space Radiation Modeling Workshop held in Boulder, CO, and is part of a larger collaborative effort to study the radiation environment on the surface of Mars. Calculated fluxes for neutrons, protons, deuterons, tritons, helions, alpha particles, and heavier ions up to Fe are compared with measurements taken by Radiation Assessment Detector (RAD) instrument aboard the Mars Science Laboratory over a period of 2 months. The degree of agreement between measured and calculated surface flux values over the limited energy range of the measurements is found to vary significantly depending on the particle species or group. However, in many cases the fluxes predicted by HETC-HEDS fall well within the experimental uncertainty. The calculated results for alpha particles and the heavy ion groups Z = 3-5, Z = 6-8, Z = 9-13 and Z > 24 are in the best agreement, each with an average relative difference from measured data of less than 40%. Predictions for neutrons, protons, deuterons, tritons, Helium-3, and the heavy ion group Z = 14-24 have differences from the measurements, in some cases, greater than 50%. Future updates to the secondary light particle production methods in the nuclear model within HETC-HEDS are expected to improve light ion flux predictions.