In this paper, a helicoid multi-groove vacuum pump (drag pump) of indirect exhaust is studied from the theoretical point of view. The motion of gas is considered within a tube of orthogonal cross-section. The pumping action is caused by moving the opposite sides with different speeds in the x-direction. At the beginning, a new term, the separation pressure between viscous and molecular states, is defined and then the theory of Gaede for the helicoid single-groove drag pump for the molecular state is extended to the helicoid multi-groove drag pump, for both viscous and molecular states. Finally, the pump characteristics are studied as a function of the helicoid step and the optimum angle for pump design is given.