In this paper, the acoustic performance of three different expansion-chamber mufflers with extended tube under space constraint is presented. A shape optimization analysis is performed using a novel scheme called Threshold Acceptance (TA), the best design obtained by the shape optimization method are analyzed by Finite Element Method (FEM). This numerical approach is based on the maximization of the sound transmission loss (STL) using the Transfer Matrix Method (TMM), a modeling method based on the plane wave propagation model. The FEM solution used to analyse the STL of the shape optimized mufflers is based on the Acoustic Power method, a standard computational code COMSOL Multiphysics is used to analyse in 3D the sound attenuation of the mufflers by the FE method. The acoustical ability of the mufflers obtained is than assessed by comparing the FEM solution with the analytical method. Results show that the maximal STL is precisely located at the desired targeted tone. In addition, the acoustical perform...