Abstract: The differences of the form and stiffness of boundary restraints do directly affect the dynamic responses and bearing capacity of structures under explosion loadings, and the existing theories are not suitable for its failure to take account of effects of flexible boundary conditions. Therefore, it is necessary to establish a new method. The model for a plate under explosion loadings with flexible edge restraints is established, and the mode functions are conducted to analyze the effects of a vertically elastic support and a damping support, the rotational constraint and the duration time of loads on displacement and internal force. The results show that the vertically elastic support and damping support can make the total displacement increase, and that the inertia force induced by the increase consumes energy, making the flexural deformations and bending moments decreased. The rotational restraints confine the rotation of the plate and decrease the maximum deformation. Therefore, the anti-explosion potential can be relatively improved by adjusting the form or stiffness of flexible edge constraints. Loading time gives its influence on the dynamic response mainly by the parameter ωt_d. With the increase of ωt_d, the bending moment will significantly increase when the parameter is smaller.