This study offers a Monte Carlo alternative for computing mass energy absorption coefficients of any material through calculation of photon energy deposited per mass of the sample and the energy flux obtained inside a sample volume. This approach is applied in this study to evaluate mass energy absorption coefficients of some amino acids found in human body at twenty-eight different photon energies between 10 keV and 20 MeV. The simulations involved a pencil beam source modeled to emit a parallel beam of mono-energetic photons toward a 1 mean free path thick sample of rectangular parallelepiped geometry. All the components in the problem geometry were surrounded by a 100 cm vacuum sphere to avoid any interactions in materials other than the absorber itself. The results computed using the Monte Carlo radiation transport packages MCNP6.2 and GAMOS5.1 were checked against the theoretical values available from the tables of XMUDAT database. These comparisons indicate very good agreement and support the conclusion that Monte Carlo technique utilized in this fashion may be used as a computational tool for determining the mass energy absorption coefficients of any material whose data are not available in the literature.