A numerical methodology is applied to investigate the flow in the channels of a molecular pump in the slip flow regime. Both the slip and the no-slip boundary conditions are used to examine their effects on the flow field and the pumping performance. Also compared is the use of a rectangular channel model and a spiral channel model. In the latter model the flow channels are placed on the rotor of the pump while the former is sited on a stationary frame. It is shown that, by comparing with the no-slip condition, the slip condition leads to a weaker reverse flow in the channel and lower compression ratio. The results of the rectangular model are close to those of the spiral model, although there exists a minor degree of difference. This demonstrates that the rotational effects can be neglected. It is shown from the analysis that a pressure gradient in the circumferential direction is caused by the diffusion of the circumferential shear stress in the radial direction. However, by the present models the resulted pressure difference between the two side walls of the flow channel remains almost as a constant, irrespective of the flow rates. This is not true in the real flow.