  The main properties of the Levi-Civita solutions with the cosmological
constant are studied. In particular, it is found that some of the solutions
need to be extended beyond certain hypersurfaces in order to have geodesically
complete spacetimes. Some extensions are considered and found to give rise to
black hole structure but with plane symmetry. All the spacetimes that are not
geodesically complete are Petrov type D, while in general the spacetimes are
Petrov type I.
