  We present the exact exterior solution for a static and neutral cylindrically
symmetric source in locally conformal invariant Weyl gravity. As a special case
the general relativity analogue still can be attained, however only as a
sub-family of solutions. Our solution contains a linear term that would thus
result in a potential that grows linearly over large distances. This may have
implications for exotic astrophysical structures as well as matter fields on
the extremely small scale.
