We investigate a class of cylindrically symmetric inhomogeneous Λ-dust spacetimes which have a regular axis and some zero expansion component. For Λ = 0, we obtain new exact solutions to the Einstein equations and show that they are unique, within that class. For Λ = 0, we recover the Senovilla-Vera metric and show that it can be locally matched to an Einstein-Rosen type of exterior. Finally, we explore some consequences of the matching, such as trapped surface formation and gravitational radiation in the exterior.