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 a is in the range 0 less than or equal to sigma less th
an or equal to 1. The mass per unit length of the shell is given expli
citly 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.