A finite-element scheme for solving wave propagation problems in devices with complete azimuthal symmetry both in their material properties and geometry is presented. The phi-coordinate variation is restricted to sin(n-phi + zeta), thus requiring only a two dimensional space for the complete finite-element analysis. The open radiating boundaries inherent in many propagation problems are tackled through simulated absorption of the radiation by lossy materials. Also proposed for these kinds of boundaries is a hybrid FEM-BEM formulation, based on the vector Green's function for the Helmholtz equation. This method has been tested by application to an open-ended circular waveguide and a comparison with the simulated-absorption results.