In this thesis, using MCNP computational code (Monte Carlo N-Particle), gamma exposure buildup factor at energies of 1 up to 100 MeV for isotropic point source with thickness from 1 to 10 mfp for water and lead have been calculated (taking into account all the interactions of photons with matter). The obtained results at low energies (up to 15 MeV), are compatible well with the results of other references that have been given in low energies and similar requirements. Then, using MATLAB software the calculated buildup factors have been fitted with Taylor (for lead), Berger (for water) and polynomial functions (for both matter), and coefficients (parameters) of these functions have been derived. Using these parameters and functions, the buildup factors can be achieved without the need for cumbersome calculations. In this study, for the first time, the gamma ray exposure buildup factors for isotropic point source water at energies 15 up to 100 MeV presented. Also, the exposure buildup factors are fitted with Taylor (for lead), Berger (for water) and the polynomial functions (for both) at energies 15 up to 100 MeV. The results can be used in the calculation of shielding for energies up to 100 MeV.