The paper aims to study dynamic acceleration response and acceleration power spectral density of a three-degree-of-freedom semi-definite system under random vibration. The mass-spring-damping system of the three degrees of freedom semi-positive definite system is established. According to the ASTM-D4728 random vibration standard in the United States, using the Matlab/Simulink simulation platform, the simulation model is established, and the parameters of the model are input, and the dynamic response under the random vibration of the three-degree of freedom semi-positive definite system is obtained. Based on the same test standard, the difference between the test results and the simulation results is compared. In the low frequency band (less than 80 Hz), the correlation coefficient between the acceleration power spectral density value of Simulink simulation and random vibration experiment reached 0.983; and the maximum difference between the two measured acceleration power spectral density values was only 8.8%. In the high frequency band (greater than 80 Hz), the correlation coefficient between the acceleration power spectral density value of Simulink simulation and the random vibration experiment only reached 0.745. However, the maximum difference between the two measured acceleration power spectral density values was 13.1%. Analyzing low frequency random vibration of packaging system with Matlab/Simulink simulation platform to analyze the low frequency random vibration of packaging system is a simple and feasible method. To some extent, it can be used as a substitute for random vibration test.