  The gravitational collapse of an infinite cylindrical thin shell of generic
matter in an otherwise empty spacetime is considered. We show that geometries
admitting two hypersurface orthogonal Killing vectors cannot contain trapped
surfaces in the vacuum portion of spacetime causally available to geodesic
timelike observers. At asymptotic future null infinity, however, congruences of
outgoing radial null geodesics become marginally trapped, due to convergence
induced by shear caused by the interaction of a transverse wave component with
the geodesics. The matter shell itself is shown to be always free of trapped
surfaces, for this class of geometries. Finally, two simplified matter models
are analytically examined. For one model, the weak energy condition is shown to
be a necessary condition for collapse to halt; for the second case, it is a
sufficient condition for collapse to be able to halt.
