This paper studies the analysis and design of a proton exchange membrane (PEM) fuel cell stack. The aim of this study is to recognize the structural behaviour of PEM fuel cell under the steady state operation by using finite element analysis (FEA). First, the solid model of the PEM fuel cell are generated by AutoCAD software with a parametric program, and then the model is imported into the ANSYS software to establish the FEA meshes. Next, a series of FEA are executed to analyze the thermal and structural behaviour of the fuel cell stack. Structural behaviour of a single-cell fuel cell stack is analyzed at the beginning. Structural and thermal boundary conditions are applied into the meshed model, including the heat generation of chemical reaction, the force convection of cooling water, and assembly pressure on the end plate. In addition, the analyses of 7-cell fuel cell stack are executed to derive the characteristics of the multiple-cell stack. Results of analyses show that temperature distribution in the fuel cell stack is non-uniform, and high structural and thermal stresses are found in the structure, which will result in the failure of the fuel cell stack, especially on the carbon plates.