  We investigate geometrical properties of 5D cylindrical vacuum solutions with
a transverse spherical symmetry. The metric is uniform along the fifth
direction and characterized by tension and mass densities. The solutions are
classified by the tension-to-mass ratio. One particular example is the
well-known Schwarzschild black string which has a curvature singularity
enclosed by a horizon. We focus mainly on geometry of other solutions which
possess a naked singularity. The light signal emitted by an object approaching
the singularity reaches a distant observer with finite time, but is infinitely
red-shifted.
