Model calculations of the particle flux on the surface of Mars due to the Galactic Cosmic Rays (GCR) can provide guidance on radiobiological research and shielding design studies in support of Mars exploration science objectives. Particle flux calculations for protons, helium ions, and heavy ions are reported for solar minimum and solar maximum conditions. These flux calculations include a description of the altitude variations on the Martian surface using the data obtained by the Mars Global Surveyor (MGS) mission with its Mars Orbiter Laser Altimeter (MOLA) instrument. These particle flux calculations are then used to estimate the average particle hits per cell at various organ depths of a human body in a conceptual shelter vehicle. The estimated particle hits by protons for an average location at skin depth on the Martian surface are about 10 to 100 particle-hits/cell/year and the particle hits by heavy ions are estimated to be 0.001 to 0.01 particle-hits/cell/year.