The nuclear magnetic shielding σ in a molecule is changed by the presence of an external uniform electric field. This change may be expressed in terms of the shielding polarizabilities σ′ and σ″. Values of σ′ and σ″ have been evaluated for H2, N2, HF and CO using a combination of the second order Møller-Plesset theory (MP2) and the finite-field perturbation theory. The effects of electron correlation on the σ′ and σ″ tensors for N2, HF and CO are seen to be sufficiently large that a higher-order theory than MP2 will be necessary to account for them fully.