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The relativistic nuclear recoil corrections to the energy levels oflow-laying states of hydrogen-like and high $Z$ lithium-like atoms in allorders in $\alpha Z$ are calculated. The calculations are carried out using theB-spline method for the Dirac equation.  For low $Z$ the results of the calculation are in good agreement with the$\alpha Z$ -expansion results. It is found that the nuclear recoilcontribution, additional to the Salpeter's one, to the Lamb shift ($n=2$) ofhydrogen is $-1.32(6)\,kHz$. The total nuclear recoil correction to the energyof the $(1s)^{2}2p_{\frac{1}{2}}-(1s)^{2}2s$ transition in lithium-like uraniumconstitutes $-0.07\,eV$ and is largely made up of QED contributions.Comment: 19 pages, latex, accepted for publication in Phys. Rev.

Relativistic nuclear recoil corrections to the energy levels of hydrogenlike and high-Zlithiumlike atoms in all orders in αZ