Abstract: The interaction between structure and granular materials exists widely in various engineering fields, and the research method of this continuum-discrete coupling problems faces numerous challenges. The composite-mapping hybrid algorithm is presented to research dynamics of continuum-discrete coupling problems. The continuum model is divided into the inner region and the border region of particle contact. In the border region, the composite spheres method is applied to construct the profile of continuum efficiently in order to facilitate fast contact detection between the continuum and particles. In the inner region, the finite element mapping method is introduced to precisely calculate the internal force and deformation of continuum, and the method also contains Rayleigh damping mapping processes. The program with the composite-mapping hybrid algorithm is developed based on the compute cluster and GPU parallel computing technique. The numerical simulation of the square vibration plate which supported at four fixed edges and buried in particles is done to study continuum-discrete coupling dynamics problems. The results show that the proposed composite-mapping hybrid algorithm is appropriate for realization of the compute cluster and GPU paralleled computing technique and improvement of computational efficiency. In analysis on buried plate problems, motion and deformation of the plate can be easily and accurately measured by means of the algorithm. Simultaneously, contact detection can be achieved rapidly in the interface between continuum and discrete, and mechanical parameters of displacement, deformation and vibration modes can also be calculated. The influence of excitation frequency and amplitude on square plate's nonlinear vibration has been studied through excitation with constant amplitude-changing frequency and with constant frequency-changing amplitude, and the period-doubling has been found. Meanwhile, the energy dissipation of granular media in this continuum-discrete coupling system is provided.