Abstract: The goal of the project is to study wormhole metrics in classical Weyl (conformal) gravity. In the first part the Kruskal-Szekeres coordinates for the Mannheim-Kazanas solution are found and the Penrose diagram of its maximal extension is found. An overview of known results about wormholes in Weyl gravity is presented. In the final part a new analytical vacuum solution of the Bach equations is introduced and the corresponding energy-momentum tensor in the presence of a Dirac field with Weyl invariant action is examined.