This present paper develops an absolute nodal coordinate formulation (ANCF) improved lower-order plate element (ILOPE) for nonlinear dynamic response analysis of thin soft silicone plates with large deflection. Different from a common linear metallic plate which is modeled by combining linear constitutive model with original lower-order plate element (OLOPE), both material nonlinearity and geometric nonlinearity should be taken into account for this type of silicone plate. An improved dynamic formulation is developed for modeling and analyzing the soft deformable silicone plate based on Yeoh nonlinear constitutive model combined with ILOPE, meanwhile the stiffening effect problem is circumvented smoothly. By bringing in penalty function, and the elastic force and its derivative matrices of Yeoh model are deduced, and then a dynamic equations of motion for the silicone plate is founded in the frame of ANCF. The second order differential dynamic equation is solved by uniting Newton–Raphson iterative approach with Newmark numerical integral method. Dynamic free-falling motion process of a half-cantilevered silicone plate and a spherical hinge silicone plate only under the influence of gravitational force are simulated by adopting OLOPE and ILOPE, respectively. The comparison of the simulation results calculated by ILOPE with those obtained by the previously proposed reduced-order plate element and commercial software ANSYS demonstrates that the improved dynamic formulation is feasible and effective. Finally, the displacement nephograms of middle surface of two types of silicone plates are elaborated in terms of displacements and configuration variations, and the law of conservation of energy is elucidated from perspective of different energy variations.