The Material Plasma Exposure eXperiment (MPEX) vacuum pumping system is responsible for creating prototypic conditions in the plasma material interaction chamber that mimic those in a fusion reactor divertor region. Additionally, the vacuum system needs to minimize the pressure in the plasma heating region to improve the coupling of the electron cyclotron heating and ion cyclotron heating to the plasma, minimizing waste heat exhausted to high heat flux components. The final design of the system has been sized to comply with the vacuum pump operating environment and to reduce the number of unique pumps required while meeting performance requirements. Bounding cases with and without the plasma present have been developed in the pumping analysis, and an initial calculation has been performed based on the plasma pumping identified in Proto-MPEX operation though this result will remain unverified until MPEX operation.