Stokes flow through a single-screw extruder driven either by an axial pressure-gradient, or by the rotation of the screw, or by a combination of both is analyzed. The geometry of the screw is chosen to resemble that encountered in the metering section of a real-life industrial extruder. Working on the simplifying assumption of large helical pitch, a perturbation analysis is performed in non-orthogonal helical coordinates, and contributions to the velocity and pressure fields are computed up to second-order by finite element methods for unidirectional and two-dimensional Stokes flow. Velocity fields are presented for different screw geometries, the axial flow rate is computed for pressure- and rotation-driven flow, comparisons with simple models are made, and the effect of the pitch on the trajectories of passively convected particles is demonstrated. In the case of purely pressure-driven flow, the flow rate decreases, whereas in the case of rotating flow the flow rate increases as the gap between the screw and the barrel is reduced.