Theoretical fluxes of gamma rays escaping the surface of Mars were calculated. These and other calculated fluxes are needed to model the counting rates in the Mars Odyssey gamma ray spectrometer that are used to determine elemental compositions and other results using these measurements. Cross sections for the formation of gamma rays by both thermal and fast neutrons were compiled and evaluated. These evaluated cross sections were used with neutron fluxes calculated with the Monte Carlo N Particle Extended (MCNPX) code to get gamma ray production rates as a function of depth in the Martian surface. The fluxes of these gamma rays as a function of angle at the Martian surface were then calculated using gamma ray attenuation coefficients.