This study aims to compute total mass attenuation coefficients of thirteen biological samples found in human body using the well-established Monte Carlo method. The simulations utilize a point photon source which emits mono-energetic photons directed as a parallel beam toward the cylindrical absorber behind which was placed a small disc-shaped vacuum detector. All the components in the problem geometry were surrounded by a vacuum sphere to avoid any interactions in materials other than the sample. In this manner, the simulation setup ensures that no scattered photons contribute to the flux in the detector. The simulations were carried out at thirty-six different photon energies between 10 keV-20 MeV. The results of this study indicate very good agreement with theoretical data and measurement values available in literature and indicate that Monte Carlo technique may be used as an alternative for calculations of mass attenuation coefficients.