The temperature driven rarefied gas flow and the pressure difference associated to this phenomenon have been numerically studied for the specific case of a multistage pump assembly consisting of a series of channels with linearly diverging, converging or uniform rectangular cross sections. Various combinations of these three geometrical configurations have been analyzed and key parameters of the pump, such as net mass flow rate and final pressure difference, have been compared. Modeling is based on the linearized Shakhov model kinetic equation with diffuse boundary conditions while the channels are modeled adequately long in order to justify the implemented infinite capillary methodology.In all configurations under investigation the characteristic curves of the net mass flow rate versus the pressure difference in terms of channel geometry, input pressure, imposed temperature ratio and number of stages have been obtained. By calculating the characteristic curves of the pump as a function of the geometry, operating conditions and number of stages, the present work provides a powerful modeling tool for the pre-sizing of a multistage Knudsen pump prototype meeting given pumping specifications. The next part of this work, which is under way, is the design of an experimental setup in order to confirm modeling results and to identify problems and constraints related to manufacturing and temperature control on the device.