We investigate the matching, across cylindrical surfaces, of static cylindrically symmetric conformally flat spacetimes with a cosmological constant $Lambda$, satisfying regularity conditions at the axis, to an exterior Linet-Tian spacetime. We prove
that for $Lambdaleq 0$ such matching is impossible. On the other hand, we show through simple examples that the matching is possible for $Lambda>0$. We suggest a physical argument that might explain these results.
