Wave propagation is one of the famous approaches for analyzing the vibration of solid structures. Literature reviews show that most bodies analyzed with this approach are one-dimensional waveguide structures. In this paper, the free vibration of annular circular and sectorial membranes are analyzed using the wave propagation approach. Firstly, the propagation and reflection matrices are derived. Then, a concise and systematic approach for obtaining the natural frequencies is presented which can be a reference for future studies. The solution obtained by this method is exactly the same as those derived by the classical method.