Preliminary shielding calculations were performed to establish the dimensions of the radiation shielding surrounding the three Spallation Neutron Source (SNS) beam stops. Steel shielding thicknesses were sized to give dose levels of 1, 2, and 5 mrem/h at the top of the shield, and, to provide enough shielding along the sides and bottom of the beam dump so that soil activation is not a problem. It was concluded that 144 in. of steel shielding is needed above the beam stop. The thickness of the concrete floor in the service building above the dump was not a part of these calculations. This shielding design is current as of January 2000.