Nuclear magnetic shieldings in first- and second-row hydrides were calculated with electron correlation taken into account through third order. The calculation was performed using London’s gauge-invariant atomic orbitals (GIAOs) and finite-field Moller-Plesset perturbation theory (FF-MPPT). Furthermore, the vibrational motion corrections to the magnetic shieldings were evaluated. It was shown that the calculated isotropic shielding constants at the experimental geometries are higher than the experimental values, but that vibrational corrections are generally negative and improve the calculated shielding constants.