Abstract: Based on a new method of finite element aided testing (FAT), the full-range constitutive relationship of ductile materials can be obtained. Thus, the distribution and evolution of stress triaxiality at the root of a funnel specimen can be obtained using the ANSYS APDL program. The analyzed results are compared with those obtained using the Bridgman correction method. The full-range constitutive relationship, fracture stress, and fracture strain of four ductile materials are given, and the laws governing the distribution and evolution of stress triaxiality at the root of funnel-shaped specimens are investigated. Based on the principle of stress triaxiality the failure mechanism of funnel-shaped specimens is discussed.