The general principles of molecular drag pumping have been understood since since W. Gaede's work in 1913, but it is curious that approximate models have not existed to explain the operation of the Gaede and Holweck molecular pumps over the range of practical application. The laminar flow model for the one-dimensional Gaede pump is now complete. One would infer that the wide channel, Holweck pump model is a two dimensional generalization of the Gaede model. This generalization has not been achieved, although some specific CFD (computational fluid dynamics) solutions have been published.@footnote 1,2@ Our analytic investigation of the Holweck case shows that there is no solution with a parallel flow field, and that compressibility introduces rotation. An approximate solution at high flow rate has been obtained for wide Holweck channels, which illustrates how these issues are resolved. A major difference between the Gaede and Holweck pumps is in the form of the leakage, which is parallel to the channel in the former, and across the channel in the latter. The problem of leakage-limited operation will be discussed. In practical cases the channel depth is small, and the the solution in this dimension is known as a case of Couette-Poiseuille flow. The Holweck geometry may then be idealized in two-dimensions, as a parallelogram lying in a plane with a drag vector of arbitrary direction. @FootnoteText@ @footnote 1@ K. Nanbu & S. Igarashi, "Three-dimensional low-density flows in the spiral grooves of a turbo-molecular pump", Computers Fluids, 21(2), pp221-228, 1992 @footnote 2@ H-P Cheng, R-Y. Jou, F-Z. Chen, Y-W. Chang, "Flow investigation of Siegbahn vacuum pump by CFD methodology", Vacuum 53, pp 227-231, 1999. "Three-dimensional flow analysis of spiral-grooved turbo booster pump in slip and continuum flow", J. Vac. Sci.. Technol. A. 18(2), 543-551, Mar/Apr 2000 .