  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 $\Lambda\leq 0$ 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.
