The linear stability of a (zero potential vorticity) circular lens (i.e., warm-core ring) is investigated for the case where the ocean surrounding the lens is of finite depth. The hydrostatic balance across the lens' interface couples the pressure variations inside the lens with those in the surrounding ocean which produces the instability. It is found that in contrast to lenses in an infinitely deep ocean which are always stable, lenses in a finite-depth ocean are unstable. For a fixed lens thickness the growth rates (instability exponents) increase with decreasing total depth. For each azimuthal wave number there exists a total (ocean) depth cutoff value above which the lens is stable and below which the lens is unstable; this cutoff value increases with wave number. In most cases, instability would occur whenever the ocean-lens depth ratio is less than 3 or 4, suggesting that actual rings in the ocean may become unstable as they approach the shore where the ocean depth is relatively small. ¿ American Geophysical Union 1990