The influence of high-frequency vibrations of one of supporting rods on the axisymmetrical thermocapillary flow in the liquid half-zone and its linear stability respective to three-dimensional perturbations in the framework of generalized Boussinesq approximation was investigated numerically. The generation of mean vorticity in dynamical boundary layers is taken into account using effective boundary conditions. The influence of amplitude of vibrations and Prandtl number at different Weber number values is considered. Calculations were carried out using the finite differences method. It is shown, that vibrations can be used to control the flow, to reduce its intensity and to stabilize it. (C) 2013 Elsevier Ltd. All rights reserved.