The umbrella type vibration of the last stage blade disk of the low pressure turbine can be induced by the external excitation which caused by the torsional vibration of the turbine-generator shafts. However, there is no applicable model for analyzing the blade disk vibration due to shift torsional vibration. According to the characteristic of umbrella type blade disc vibration, a blade model for analyzing the vibration of the long blades during the torsional vibration of the shafts is given in this paper. A parameter adjusting method based on sensitivity analysis is presented so as to make the inherent characteristic of the blade disc model close to that of the real blade disc.