The Monte Carlo simulation method has been applied to generate the first data for bremsstrahlung buildup factor (BBUF) produced by the complete absorption of beta particles in different materials. The bremsstrahlung buildup factor was computed by the present method for different thicknesses of water, concrete, aluminum, tin and lead at the maximum bremsstrahlung energy of 2.2 MeV for 90Sr/90Y beta source. A computer program "BBF" was designed and improved to perform the calculations which solve the classical problem of a gamma ray reflection and transmission, the basic idea of this program is to create a series of life histories of the source particles using random sampling technique to sample the probability laws that describe the real particle's behaviour, and to trace out the particle's 'random walk' through the medium. The effect of some considered parameters like the simulation parameters and physical parameters were studied. The bremsstrahlung buildup factor has been calculated for single layer shield. The simulation results indicate the following remarks: The bremsstrahlung buildup factor increases with the increase of thickness of the shield. The bremsstrahlung buildup factor for low atomic number material is lower than that for a high atomic number material at the same source energy. The relation between the bremsstrahlung buildup factor BBUF with the atomic number Z and thickness X of the shielding material is suggested to follow the semi-empirical formula: BBUF = 1 + (a1 Z + a2) X (a3 Z + a4) where a1, a2, a3 and a4 are fitting parameters depends on the bremsstrahlung energy distribution. For 90Sr/90Y bremsstrahlung, these parameters are: a1 = 0.0007, a2 = 0.0022, a3 = 0.0072 and a4 = 0.4204.