Buildup factors are important data in radiation shielding which correct the response to uncollided photons so as to include the contribution of the scattered photons and secondary sources. It is very important to know buildup factors for various materials and their combinations used as shields. In this thesis,first we computed gamma ray exposure buildup factors using the MCNP code (Monte Carlo N-Particle code System ). in the MCNP model,a point monoenergitic isotropic source with energy from 0.3 to 10 MeV was placed at the center of the first spherical material surrounded by a second one. The first shielding material was Water and the second one was Lead. The total thickness of the shield varied between 2 to 10 mfp. As well as primary interactions such as photoelectric effect, Compton scattering, and pair production, we considered effect of bremsstrahlung and coherent (rayleigh) scattering. Then the MCNP computed data were analized by ploting the buildup factor as a function of each independent variable (energy, first material thickness and second material thickness) and obsorbing the trends. Based on the trends, we tested many different expressions with different number of constants. By MINUIT the fortran code, the constants were calculated which give the best agreement between the MCNP-computed exposure buildup factor and that obtained by formula. Trying on many expression,at last we developed a polynomial formula with 11 constants that reproduce exposure buildup factors for two layer shields with relative error (and compared with the MCNP results) below 2% . Keywords: Gamma ray, Layer of Water, Layer of Lead, Exposure Biuldup factor, MCNP code, MINUIT the fortran code