The drag on a two‐dimensional cylinder located unsymmetrically between parallel planes is calculated for low Reynolds numbers. The presence of the walls has the mathematical effect of rendering Stokes' approximation uniformly valid. In physical terms, the drag is shown to be independent of the Reynolds number and dependent on cylinder diameter, channel width, and relative fluid velocity at the cylinder axis. The drag is calculated by perturbation methods and is shown to be independent of the fluid shear to the order of approximation given. Thus the solution is applicable to a wide range of boundary conditions. The analysis is compared with the results of two experimental investigations employing radically different shear flows.