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The electrostatic Lorentz force acting on the H and C nuclei of abenzene molecule in the presence of a strong magnetic field with fluxdensity B has been estimated via Rayleigh-Schr¨dinger perturbation otheory to second order in B. In stationary conditions, a new equilib-rium configuration is reached, at which the total force has been entirelytransferred to the nuclei, and the force on the electrons vanishes. Thedistortion of the molecular geometry is rationalized in terms of third-rank electric hypershielding at the nuclei, induced by strong magneticfields applied along three Cartesian axes. The nuclear hypershieldinghas been evaluated at near Hartree-Fock level of accuracy by its defi-nition within the Rayleigh-Schr¨dinger perturbation theory, and by a opointwise procedure for the geometrical derivatives of magnetic sus-ceptibilities. The connection between these two quantities is providedby the Hellmann-Feynman theorem. A field along the C6 symmetryaxis causes a symmetric contraction of the carbon ring and an elon-gation of the CH bonds. A field along one of the C2 symmetry axiscontaining two CH bond acts to shorten them, to widen the ring, andto bend the four remaining CH bonds towards C2 . A field along one of the C2 symmetry axis through the midpoint of two opposite CCbonds causes a spindle-effect, by squeezing the molecule toward thecenter of mass. Constraints for rotational and translational invarianceand hypervirial theorems provide a natural criterion for Hartree-Fockquality of computed nuclear electric hypershielding. However, themolecular distortion is negligible for applied fields usually available ina laboratory.