  The relativistic nuclear recoil corrections to the energy levels of
low-laying states of hydrogen-like and high $Z$ lithium-like atoms in all
orders in $\alpha Z$ are calculated. The calculations are carried out using the
B-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 recoil
contribution, additional to the Salpeter's one, to the Lamb shift ($n=2$) of
hydrogen is $-1.32(6)\,kHz$. The total nuclear recoil correction to the energy
of the $(1s)^{2}2p_{\frac{1}{2}}-(1s)^{2}2s$ transition in lithium-like uranium
constitutes $-0.07\,eV$ and is largely made up of QED contributions.
