  This paper is devoted to compute the energy-momentum densities for two exact
solutions of the Einstein field equations by using the prescriptions of
Einstein, Landau-Lifshitz, Papapetrou and M\"{o}ller. The spacetimes under
consideration are the Weyl-Lewis-Papapetrou and the Levi-Civita metrics. The
Weyl metric becomes the special case of the Weyl-Lewis-Papapetrou solution. The
Levi-Civita metric provides constant momentum in each prescription with
different energy density. The Weyl-Lewis-Papapetrou metric yields all the
quantities different in each prescription. These differences support the
well-defined proposal developed by Cooperstock and from the energy-momentum
tensor itself.
