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A new method is presented to analyze multi-degree-of-freedom (MDOF) dynamic systems subjected to an external shock excitation. A two-degree-of-freedom theoretical system with linear characteristics is exemplified to illustrate the procedure of this method. The equations of motion of the dynamic system are established via matrix method. The dynamic responses of the dynamic system under an external shock excitation of a half-sine type are obtained by MATLAB and ANSYS. It is proved that the new method is helpful to analyze MDOF dynamic systems.