Several recent papers discuss a viscous micropump consisting of Poiseuille flow of fluid between two plates with a cylinder placed along the gap perpendicular to the flow direction (e.g. Sen, Wajerski & Gad-el-Hak 1996). If the cylinder is not centred, rotating it will generate a net flow and an additional pressure drop along the channel, due to the net tangential viscous stresses along its surface. The research reported here complements existing work by examining the lubrication limit where the gaps between the cylinder and the walls are small compared to the cylinder radius. Lubrication analysis provides analytical relations among the flow rate, torque, pressure drop and rotation rate. Optimization of the flow parameters is shown in order to determine the optimal geometry of the device, which can be used by micro-electrical-mechanical systems designers. It is also shown, for example, that a device cannot be developed that achieves maximum flow rate and rotation simultaneously. In addition, since the Reynolds number can be smaller than 1, the Stokes equations are solved for this configuration using a numerical boundary integral method. The numerical results match the lubrication solution for small gaps, and determine the limits of validity for using the lubrication results.