A series of dose rate calculations in two-layered slab shields has been performed, using a Monte Carlo technique, at combinations of source energy and slab thickness selected with the aid of a composite experiment design. Least-squares fits to the dose buildup factors obtained from these calculations yield equations in which the dose buildup factor is represented as a quadratic function of the source energy and the thicknesses of the materials composing the shield. The accuracy of these equations has been established by comparisons with existing data.