Abstract: Compared to traditional vacuum pumps, the Knudsen vacuum pump, based on the thermal transpiration effect, is paid lots of attention to because of the advantages of no moving parts and simple structure. The Knudsen vacuum pump is commonly used by type of many unit pumps in series. According to the energy consumption and efficiency model of the single-stage Knudsen vacuum pump and focusing on the relationship of the number of stages with heat transfer and pressure distribution, energy consumption (heat requirements per pumped molecule) and operation efficiency model are established for multistage Knudsen vacuum pump when the pumped gas medium is in transition flow regime. Furthermore, the investigation is carried out on correlations between heat requirements per pumped molecule and operating efficiency and those parameters such as number of stages, Knudsen number, pressure ratio and temperature difference. The results show that as the Knudsen number increases from 0.2 to 8, the corresponding optimum number of stages decreases from 118 to 15. As the pressure ratio increases from 2 to 100, the corresponding optimum number of stages increases from 12 to 77. As the temperature difference increases from 50 K to 350 K, the corresponding optimum number of stages decreases from 68 to 15. The larger the Knudsen number (temperature difference) or the smaller the pressure ratio, the lower the heat requirements per pumped molecule (the higher the operating efficiency) and the smaller the corresponding optimum number of stages as well as the minimal number of stages required. Considering the design of a multistage Knudsen vacuum pump from the perspective of energy efficiency optimization, it is necessary to take into account the comprehensive effects of Knudsen number, pressure ratio and temperature difference in order to determine the range of optimum number of stages.