Stress triaxiality is a key factor in controlling the fracture of materials. Based on new method of finite element aided testing（ FAT）,the full-range constitutive relationship of ductile materials could be obtained. Thus,the distribution and evolution of stress triaxiality at the root of a funnel specimen is able to be obtained by ANSYS APDL program. The comparison of the analyzed results with those obtained by Bridgman correction method is completed and the failure mechanism of funnel-shaped specimen is discussed. The full-range constitutive relationship,fracture stress,fracture strain of the four ductile materials are given. Therefore,the law of the distribution and evolution of stress triaxiality at the root of funnel-shaped specimens are investigated.