A one-dimensional gamma-ray transport code BIGGI 4T has been used to calculate gamma-ray attenuation in single layer and multiple layers of lead and water slabs from a plane monodirectional source. It has been found that boundary effect of finite medium is appreciable only in water within two mean-free-paths (mfp) of the boundary. Transmission buildup factors for multilayer slabs are not sensitive to the sequence of the alternate layers for the 3-MeV source. The conventional rule of thumb, that when the outermost layer exceeds 2 or 3 mfp, the buildup factor of the outermost material generally recommended, has been shown to be a bad approximation when based on the total number of mean-free-paths along the line of sight through all materials. Energy absorption buildup factor at the interface between layers was investigated in more detail. Transmission buildup factors obtained in the present study have been compared with those calculated by other empirical formulas. The applied range of various empirical formulas has been discussed. It has been found that semiempirical formulas devised by Kalos give data agreeing, in general and on the average, with the present results to within 5%.