The steady flow in rectangular cavities is investigated both numerically and experimentally. The flow is driven by moving two facing walls tangentially in opposite directions. It is found that the basic two-dimensional flow is not always unique. For low Reynolds numbers it consists of two separate co-rotating vortices adjacent to the moving walls. If the difference in the sidewall Reynolds numbers is large this flow becomes unstable to a stationary three-dimensional mode with a long wavelength. When the aspect ratio is larger than two and both Reynolds numbers are large, but comparable in magnitude, a second two-dimensional flow exists. It takes the form of a single vortex occupying the whole cavity. This flow is the preferred state in the present experiment. It becomes unstable to a three-dimensional mode that subdivides the basic streched vortex flow into rectangular convective cells. The instability is supercritical when both sidewall Reynolds numbers are the same. When they differ the instability is subcritical. From an energy analysis and from the salient features of the three-dimensional flow it is concluded that the mechanism of destabilization is identical to the destabilization mechanism operative in the elliptical instability of highly strained vortices.