  We investigate static cylindrically symmetric vacuum solutions in Weyl
coordinates in the framework of f(T) theories of gravity, where T is the
torsion scalar. The set of modified Einstein equations is presented and the
fourth coming equations are established. Specific physical expressions are
assumed for the algebraic function f(T) and solutions are obtained. Moreover,
general solution is obtained with finite values of u(r) on the axis r = 0, and
this leads to a constant torsion scalar. Also, cosmological constant is
introduced and its relation to Linet-Tian solution in GR is commented.
