  In this article we present a theoretical construction of spacetimes with a
thin shell that joins two different local cosmic string geometries. We study
two types of global manifolds, one representing spacetimes with a thin shell
surrounding a cosmic string or an empty region with Minkowski metric, and the
other corresponding to wormholes which are not symmetric across the throat
located at the shell. We analyze the stability of the static configurations
under perturbations preserving the cylindrical symmetry. For both types of
geometries we find that the static configurations can be stable for suitable
values of the parameters.
