In this paper the pumping mechanism of a single stage of a turbomolecular pump (TMP) is addressed. A collisionless gas, a Maxwellian distribution of particles at the inlet and outlet surfaces of the passage, and diffuse reflection for the particles that collide with the walls of the passage are assumed. Models of this type have, until now, only been applied to the two-dimensional (2D) case, i.e., the TMP stage was approximated by an infinite row of blades. This approximation can only be valid for very narrow passages, far from the axis of rotation. In the present work the 2D case has been assessed in detail as a basis for confidence in three-dimensional (3D) modeling. The main difficulties in modeling the 3D case arise from the geometric complexity and the rotating frame of reference. As a result of the latter, particle orbits are no longer straight lines, and their intersection with the walls has to be calculated iteratively The Monte Carlo method was chosen to model the 3D case as it appears to have significant advantages. The passage is divided into layers normal to the axis of rotation, and a particle proceeds at every time step to the next or previous layer. This technique of tracking saves computer time as it takes advantage of certain characteristics of the rotational system, Results for different types of blade passages are presented.