In this work we propose to develop a computational strategy based on the use of Finite Element Methods (FEM) for articulatory speech synthesis. In this context, we follow a bottom-up strategy to deal with the physics involved in speech generation. First, we solve the acoustic wave equation using FEM in space and nite di erences in time. Next, boundary losses due to viscous friction and heat conduction are taken into account. Then, a radiation condition is introduced to simulate outward propagation waves to freespace. A Perfectly Marched Layer (PML) is used for this purpose. Finally we apply the nite element method to the vowel synthesis problem, taking as an example the case of vowel /e/. The quality of the results is analyzed by means of ob jective measurements.