We propose a new method for an auto-meshing algorithm for an acoustic analysis of the vocal tract using the Finite Element Method (FEM). In our algorithm, the domain of the 3 dimensional figure of the vocal tract is decomposed into two domains; one is a surface domain and the other is an inner domain in order to employ the overlapping domain decomposition method. The meshing of surface blocks can be realized with smooth surfaces using a NURBS interpolation. We show the example of the meshes for the vocal tract figure of Japanese vowel /a/, and the trial result of the FEM simulation.