Two wavy plates, separated by a viscous fluid, move relative to each other in a direction normal to the corrugations. Assuming small‐amplitude corrugations and low Reynolds number, the unsteady Navier–Stokes equations are solved by perturbations. It is found not only that the mean drag is increased, but that an unsteady drag and an unsteady lift are also induced by the corrugations. These fluid‐induced vibrations, predicted for the first time, may be important in the design of grooved sliders.