The nuclear magnetic shielding constant has calculated for He-isoelectronic series (Z=2to10), Li-isoelectronic series (Z=3to5), Be and Li-1 by using RHF method and Data published by Andrew W. Weiss 1963) , Cleminty and Roetti (1974) . The calculations of must go through calculating many properties, so that, Electron radial density distribution and one particle expectation value are calculated, with power equal to -2, -1, 0,1and 2. For checking the results the energy are calculated for all studied atoms and ions and all results are restricted with normalization conditions. Electronic density at the nucleus and Stander deviation are calculated. All introduced results physically analyzed to find the idea behind these data. These calculations are made by using mathcad program version 11 By using PC (Pentium 4) and all results are in atomic unite (a.u.).