The phenomenon of wave propagation in periodic structures is first introduced focusing the attention on the wave characteristics - e.g. propagation constants - which help to best understand the physic of the problem. The Wave Finite Element Method (WFEM) is then discussed and two different approaches to structural modeling are described: the Dynamic Stiffness Matrix (DSM) and the Wave Amplitude (WA). An example of a simply supported beam, solved by the WA approach, is presented to outline the main steps of application the WFEM. The method is further extended to account for the presence of intermediate support along the structure. This application of the WFEM to this case study is a new development that represents the main core of the thesis.