  The gravitational collapse of a thick cylindrical shell of dust matter is
investigated. It is found that a spacetime singularity forms on the symmetry
axis and that it is necessarily naked, i.e., observable in principle. We
propose a physically reasonable boundary condition at this naked singularity to
construct the solution including its causal future. This boundary condition
enables us to construct the unique continuation of spacetime beyond the naked
singularity and ensures that the dust shell passes through the naked
singularity. When the cylindrical shell leaves its symmetry axis away, the
naked singularity disappears, and regularity is recovered. We construct
numerical solutions with this feature. This result implies that the gravity
produced by a thick cylindrical shell of dust is too weak to bind the shell
even if it engenders the formation of a curvature singularity which is so
strong as to satisfy the limiting focusing condition. For this reason, this
naked singularity is very weak in the extended spacetime; the metric tensor is
$C^{1-}$ even at the naked singularity, and the extended spacetime is complete
for almost all geodesics. This feature is also seen for singular hypersurfaces.
Such an extended spacetime can be regarded as phenomenological in the sense
that it is valid if the relevant microphysics length scale is sufficiently
small compared to the scale of interest.
