A nonlocal theory of the Rayleigh-Taylor instability, which includes the effect of a transverse velocity shear, is presented. A two-fluid model is used to describe an inhomogeneous plasma under the influence of gravity and sheared equilibrium flow velocity and to derive a differential equation describing the generalized Rayleigh-Taylor instability. An extensive parametric study is made in the collisionless and collisional regimes, and the corresponding dispersion curves are presented. The results are applied to the equatorial F region and to barium releases in the ionosphere.