The mechanical design of the vacuum pumping systems for SNS DTL (Drift Tube Linac) and CCL (Cavity Coupled Linac) linac systems is summarized. Both vacuum systems were modeled to select the optimal pump configuration. The pressure history in up to 182 sub-volumes was analyzed in detail. Included in the model are time-dependent outgassing rates and pressure-dependent pump speeds for a variety of gas species. With this information, we solved for the pressure history during roughing and with turbo and ion pumps. The number and size of each pump were optimized to achieve the desired pressure with minimal costs. In the optimized design, directly mounted ion pumps were provided for six DTL tanks. For four CCL modules (each in length of 12-15 m), ion pumps with manifolds were selected. With all metallic surface outgassing, seal leakage and expected gas loads from all diagnostic devices taken into account, the designed systems can provide operating drift-tube pressure below 1.8 x 10{sup -7} Torr and CCL beamline pressures below 9.2 x 10{sup -8} Torr even under abnormal conditions. Details of the design and the modeling results are presented.