  Relativistic thick ring models are constructed using previously found
analytical Newtonian potential-density pairs for flat rings and toroidal
structures obtained from Kuzmin-Toomre family of discs. In particular, we
present systems with one ring, two rings and a disc with a ring. Also, the
circular velocity of a test particle and its stability when performing circular
orbits are presented in all these models. In general, we find that regions of
non-stability appear between the rings when they become thinner.
