  In this paper, we find the teleparallel version of the Levi-Civita metric and
obtain tetrad and the torsion fields. The tensor, vector and the axial-vector
parts of the torsion tensor are evaluated. It is found that the vector part
lies along the radial direction only while the axial-vector vanishes everywhere
because the metric is diagonal. Further, we use the teleparallel version of
M$\ddot{o}$ller, Einstein, Landau-Lifshitz and Bergmann-Thomson prescriptions
to find the energy-momentum distribution of this metric and compare the results
with those already found in General Relativity. It is worth mentioning here
that momentum is constant in both the theories for all the prescriptions. The
energy in teleparallel theory is equal to the corresponding energy in GR only
in M$\ddot{o}$ller prescription for the remaining prescriptions, the energy do
not agree in both theories. We also conclude that M$\ddot{o}$ller's
energy-momentum distribution is independent of the coupling constant $\lambda$
in the teleparallel theory.
