The numerical model for opposite-side simple-support-free rectangular plate is established based on the theory of engineering vibration. The basic differential equation of transverse vibration of thin plate and the method of development of trigonometric function series are being used to analyze the behaviors of rectangular plate under moving area-loads in constant speed. The analytical solution of dynamic response for plate was obtained. This model can be used to simulate the dynamic response for thin plate under moving shock load and to assess the yield state of thin plate under shock loads. The Mises' yield criteria was used to judge the dynamic yield case of plate under shock loads. The distribution of stress and strain of dynamic response in parent plate under shock loads was solved according to the free-simple harmonic oscillation equation of plate. The calculation results can be used to analyze the plastic area and visco -plastic area of stress distribution in the plate. It is of some guiding significance for the installation structure of parent plate in explosive welding.