Recent studies have shown the possibility to manipulate small elastic spheres in 3D with a single-sided beam. Acoustical tweezers are very appealing because they provide a fine spatial control of the motion of a single particlehttps://dx.doi.org/10.1016/j.ultras.2020.106296 in space. Their main limitations are due to the weak restoring axial force and improving this force is still a challenge. We show theoretically that the spherical vortex beams can trap large particles and enhance the axial force. Indeed, the special features of these unusual beams look like the bottle beams in optics. Nevertheless, their spatial complexity presupposes that they can be produced with sufficient precision. Therefore, attention is paid to the synthesis of the spherical vortices. A method based on the inverse filter method is proposed. It allows to synthesize them with a very good precision since the theoretical force is recovered experimentally with an error smaller that than 10%. Then, the spherical vortices are used to trap polyethylene beads with radii between 500 and 590 µm. Experiments show that the radial trap is working while no beads have been trapped in the axial direction. This failure is analyzed in detail and is shown to be mainly due to sensitivity to the properties of the materials which influences the resonance modes of the elastic sphere. This study paves the way to the optimization of acoustical tweezers for the manipulation of large objects.