In general relativity, cylindrical solutions have been used to study various fields like cosmic strings. Examples of these solutions are the Levi-Civita (LC) spacetime, which describes the vacuum field exterior to an infinite cylinder of matter, and its generalization to include a cosmological constant, the Linet-Tian (LT) spacetime. In this talk, an analysis of the geodesic motion in the LT spacetime is presented and the dynamics of the geodesics is compared with those of the geodesics in the LC spacetime. In particular, the effects are analysed that the introduction of a positive or negative cosmological constant has on the orbits' stability. Furthermore, the matching of the LT solution to other non-vacuum solutions, producing a globally regular cylindrically symmetric solution, is discussed.