In the mid-frequency range, numerical methods such as the finite and boundary element methods are not the most suitable for structural dynamic analysis as mesh refinement leads to models that are often too large. Other methods that can be considered as semi-analytical, such as the spectral element method, do not need that at higher frequencies a mesh refinement be done, but they are limited in the geometries that can be modeled and some of its formulation cannot treat arbitrary boundary conditions. This work develops a spectral element for thin plates based on a high precision finite element proposed by Kulla, which can be applied on modeling plates with arbitrary boundary conditions. The results obtained are compared with others from different methods presented in the literature Ver menos