The Buildup Factor for gamma ray in two materials, water and lead, has been calculated by using the Monte Carlo Method. A computer program "MONTRAY" was designed and implemented to perform the calculations. The program can be considered as a flexible utility for simulating the classic problem of a gamma ray beam incident on an infinite plane slab of an absorbing material. The problem of a gamma ray beam incident on an infinite plane slab of absorbing material can be handled theoretically by using the statistical "probability" theory, and it is utilized in gamma transport problem. The penetration of radiation could be modeled compiling the life histories of individual Gamma rays as they move about, from the point where they either are partially absorbed in the shield or pass through it. The effects of some considered parameters like simulation parameters, number of iteration, number of energy interval divisions were studied in this work. The buildup factor has been calculated for two cases:Single layer shield. 2.Double layer shield by using the Kalos Method. For the case of a single layer shield, some factors, like the atomic number, energy, and thickness have been studied. The simulation results indicated the following remarks: The buildup factor increases with the increase of thickness of the shield. A high increase of buildup factor occurs with low atomic number, in which one can observe that at a heavy material the buildup factor increases slowly. The buildup factors for low atomic number material is higher than those ,for high atomic number materials for the same source energy. Build up factor for water at source energy 0.662 MeV is greater than that for source energy 1.25 MeV, but for lead (high Z-material) the behavior is reflected since the buildup factor for lead at energy 1.25 MeV greater than the buildup factor for lead at energy 0.662 MeV. This behavior can be justified as follows The increase in the energy led to increase in the penetration of the photons in the materials and it leads to an increase in the probability of scattering, which in turn play an important rule in increasing the buildup factor. Buildup Factor for a slab geometry consisting of a layered system was studied. In this work Kalos method was applied to study the gamma ray buildup factor in (lead-water) and (water-lead) layer for plane mono directional gamma ray source. The behavior of the buildup factor for slab geometry double-layered system can be described as follows: In the first layer, the buildup factor is exactly the same value that for an infinite medium of the first layer, but suffers a material change effect near the layer interface. Entering the second layer, the Buildup departs from the value for an infinite medium of the first layer then parallels the values for an infinite of the second material. The Buildup factor in the second layer lies between those for single media of both component materials.