  The Levi-Civita (LC) solution is matched to a cylindrical shell of an
anisotropic fluid. The fluid satisfies the energy conditions when the mass
parameter $\sigma$ is in the range $0 \le \sigma \le 1$. The mass per unit
length of the shell is given explicitly in terms of $\sigma$, which has a
finite maximum. The relevance of the results to the non-existence of horizons
in the LC solution and to gauge cosmic strings is pointed out.
