The goal of this paper is to propose a general finite element method (FEM) for sound propagation and vibro-acoustic problems in the presence of swirling ducted flows. The numerical method has already been successfully tested for sheared flows in the authors' recent papers. The acoustic variational formulation is based on a non-standard wave equation established by Galbrun in 1931, which describes exactly the same physical phenomenon that the linearized Euler's equations (LEE). Though this equation is only written in terms of the Lagrangian perturbation of the displacement, a mixed pressuredisplacement formulation is preferred in order to avoid a locking phenomenon. Furthermore, the coupling conditions for vibro-acoustic problems are naturally introduced. The FEM method proposed in this paper is compared in the axisymmetric case to a semi-analytical model, which is a generalisation of Pridmore-Brown equation to a duct with swirling flows and vibrating walls. A first set of results is compared with semi-analytical solutions for a rigid wall duct. A second set of results concerns the vibroacoustic interactions of a straight duct with an elastic outer wall.