A vibrated drop constitutes a very rich physical system, blending both interfacial and volume phenomena. A remarkable experimental study was performed by M. Costalonga (PhD. Université Paris Diderot, 2015) highlighting sessile drop motion subject to horizontal, vertical and oblique vibration. Several intriguing phenomena are observed such as drop walking and rapid droplet ejection. We perform three-dimensional direct numerical simulations of vibrating sessile drops where the phenomena described above are computed using the parallel multiphase code BLUE. The fluid interface solver is based on a parallel implementation of a hybrid Front Tracking/Level Set method designed to handle highly deforming interfaces with complex topology changes. We developed parallel GMRES and multigrid iterative solvers suited to the linear systems arising from the implicit solution for the fluid velocities and pressure in the presence of strong density and viscosity discontinuities across fluid phases.