As a new type of meshless method which has appeared in recent years, the Reproducing Kernel Particle Method has such meshless features as the need for nodes only without classified units, and is advantageous in the process of calculation. The present study introduces the Reproducing Kernel Particle Method and applies it to the research of nonlinear dynamic mechanics. The dynamic process involves different kinds of nonlinearity. The study assumes that deformation of dynamic analysis belongs to small one and that the material nonlinearity has been taken into account. When under small strain, the increment constitutive law and the total Lagrangian model of calculation are adopted to deduce the dynamic control equation by the Reproducing Kernel Particle Method. The instances of calculation demonstrate that this method is effective in the analysis of dynamic problems.