The work aims to obtain the damage boundary of product with multiple critical components under rectangular impact, and analyze the change rules and influencing factors of the damage boundary under linear and nonlinear (tangent and hyperbolic tangent) conditions. First, the lumped mass method was adopted to establish a MDOF discrete packaging product system model. Second, the kinematic equations of the system were derived according to the Newton's second law, and dimensionless dynamic equations of the system were obtained through dimensionless processing. Third, the dynamic response of the system was solved according to the fourth-order Runge-Kutta method, and the damage boundary was obtained. The results showed that compared with linear packaging materials, hyperbolic tangential buffer packaging materials could expand the non-damaged zone of the package, while tangential buffer packaging materials could expand the non-damaged zone, and the influence degree was proportional to the nonlinear parameters. In some cases, the damage boundary curves of different critical components were intersected. In conclusion, different types of impact will lead to the damage of different critical components, and the protection of all critical components should be considered in the actual logistics process.