Author's internet addresses respectively: mfas@on.br, lherrera@conicit.ve, fmpaiva@on.br and nos@on.br. 1 AbstractWe consider two exact solutions of Einstein's field equations corresponding to a cylinder of dust with net zero angular momentum. In one of the cases, the dust distribution is homogeneous, whereas in the other, the angular velocity of dust particles is constant [1]. For both solutions we studied the junction conditions to the exterior static vacuum Levi-Civita spacetime. From this study we find an upper limit for the energy density per unit length σ of the source equal . We also find that the cluster of homogeneous dust has a superior limit for its radius, depending on the constant volumetric energy density ρ 0 .