This paper deals with the effects of vibrations on the stability of a binary alloy solidifying at constant velocity under zero gravity conditions or in the presence of a static gravitational field. The density dependence of the solute concentration is accounted for through the Boussinesq approximation. In the first part of the paper, the effect of finite frequency vibrations normal to the planar interface is studied numerically. It is found that at large frequencies vibrations have a destabilizing effect. For lower frequencies, a parameter range is found where vibrations exert a strong stabilizing effect. In the second part of the paper, the influence of high-frequency vibrations is studied. Equations for the average velocity and concentration fields are obtained by a multiple scale method. It is found that vibrations normal to the interface exert a destabilizing effect, whereas tangential vibrations may suppress the onset of morphological stability. (c) 2007 Published by Elsevier B.V.