2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/211632We study static cylindrically symmetric vacuum solutions in Weyl coordinates in the context of the metric f(R) theories of gravity. The set of the modified Einstein equations is reduced to a single equation and it is shown how one can construct exact solutions corresponding to different $f(R)$ models. In particular the family of solutions with constant Ricci scalar ($R=R_{0}$) is found explicitly which, as a special case (R=0), includes the exterior spacetime of a cosmic string. Another new solution with constant, non-zero Ricci scalar is obtained and its possible relation to the Linet-Tian solution in general relativity is discussed.13 pages, RevTex, Typos corrected and references addedGeneral Relativity and Quantum Cosmologytext