The process to produce trimethoxysilane involving the reaction of methanol with silicon produces a mixture of unreacted methanol and trimethoxysilane that requires separation so that the methanol can be recycled back to the reaction section. This binary mixture forms a maximum-boiling homogeneous azeotrope of 28.65 mol % methanol at 1 bar and 87.94 degrees C. The composition of the azeotrope changes fairly significantly with pressure, so separation into high-purity component streams is viable using pressure-swing distillation. The purpose of this paper is to design a pressure -swing distillation process for this separation that uses heat integration of the two columns, which operate at different pressures and different temperatures. One of the unique features of this system is the use of a vacuum column in which tray pressure drop has a significant effect on the optimum selection of design parameters such as the number of trays. The specifications for the bottoms compositions must be adjusted as pressures are changed so as to not get too close to or too far away from the azeotropic compositions. The economic optimum design has two columns operating at 7 and 0.25 bar with an auxiliary reboiler used on the low-pressure column. Feed composition strongly impacts the economics but not the basic process topology and operating conditions.