The weighing instrument measures the weight mainly by the use of the strain foil as measuring transducer, which is attached to a stubby beam. The measured time is prolonged because of the beam vibration in the weighing process. The beam of weighing instrument was in accordance with the Timoshenko beam model, because the solution of theoretical model of free vibration of Timoshenko cantilever beam was very complex, the analysis of cantilever beam of weighing instrument was taken by the finite element method (FEA) quite easy, and then which results were taken to curve fitting. Through the force of dimensionless according to the fitting equation of beam, the index of Kurtosis was obtained. The corresponding relationship between Kurtosis and level of beam vibration was applied to measurement, which shortened the time of measurement in weighing instrument. The results show that it can determine the beam stress quickly when taking kurtosis as dimensionless index which related to the beam force, the measurement is precise with high rationality.