The non-Gaussian characteristics of product response in three-layer stacked packaging unit in random vibration were studied, and the reasons for non-Gaussian response were discussed. The results showed that, in the case of unconstrained condition, a jumping happened in the top packaging layer, and the probability density of product acceleration response was of non-Gaussian distribution. The probability density of acceleration response of product in middle layer had a certain deviation from Gaussian distribution, while the acceleration response of bottom product was close to Gaussian distribution. In the case of elastic constraint, the probability density of product acceleration response in the top packaging layer had a significant deviation from Gaussian distribution when the vibration intensity was greater. In the case of fixed constraint, the acceleration response of all products was consistent with Gaussian distribution.