This paper deals with meniscus deformation and flow in an isothermal liquid bridge maintained between two circular rods, when one rod is subject to axial monochromatic vibrations. It concerns a fundamental aspect of the problem of crystal growth from melt by the floating-zone technique which is often considered in weightlessness conditions. In the absence of vibrations the bridge is cylindrical; but due to vibration the mean shape of the meniscus is no more cylindrical and the meniscus oscillates around this mean shape. Two models are developed. First, we take into account the pulsating deformations of the meniscus (free surface), but we assume that the mean shape of meniscus remains cylindrical (i.e., we neglect the influence of vibration on this mean shape). For this simple case, a solution of the problem for the pulsating meniscus deformations and the pulsating velocity field is found in explicit form. For the mean flow, the problem is solved numerically by a finite-difference method. The calculations demonstrate the contribution of two basic mechanisms of mean flow generation due to vibrations, related to the generation of mean vorticity in the viscous boundary layer near the rigid boundaries and surface-wave propagation at a free surface. The intensity of the mean flow induced by surface waves is found to be sharply increasing when the vibration frequency approaches the resonance values that are determined from the explicit form of the solution of pulsation problem. In the second model, we take into account both pulsating and mean deformations of the meniscus. The governing equations for the potential of pulsating velocity and mean velocity, and for the pressure, are solved by using a finite-difference method and a boundary-fitted curvilinear coordinate system fitting the free surface.