Surface and interfacial waves in two superposed horizontal inviscid fluids of finite depths are studied. The flow is induced by translating a vertical rigid plate with a prescribed velocity. Analytical solutions that accurately predict the motion of the free surface and the interface are obtained by using a small-Froude-number approximation. Three different velocities of the plate are considered, while flows induced by any arbitrary motion of the plate can be easily analyzed by a linear superposition of the solutions obtained. It is shown that pinching of the upper layer can occur for a sufficiently thin upper layer, which leads to its rupture into small segments. Other interesting phenomena, such as primary and secondary wiggles generated on the interface near the wavemaker, are discussed.