Numerical Hartree-Fock wave functions for neutral atoms (for the ground state) calculated by Froese [ 11 have been used to calculate nuclear magnetic shielding constants (u) for all the atoms from helium (2 = 2) to radon (2 = 86). From the analysis of the partial contributions to Q from the various shells in xenon it is pointed out that the innermost shells make the largest contribution in agreement with the observation of Malli and Fraga [2] reported earlier.