The dynamic meshing characteristics of gear drives have been a major concern in the design of power transmission systems as they affect vibration, acoustic noise, durability and efficiency. Gaining a more comprehensive understanding of the dynamic meshing characteristics of continuous engaged gear drives is a key to the development of power transmission systems. In this paper, a dynamic contact finite element analysis method, considering the variation of the engaged teeth pairs, the loaded elastic and contact deformations, and the sliding friction, is presented for the dynamic meshing characteristics analysis of continuous and elastic engaged gear drives. Various kinds of continuous engaged gear models under low and high speed condition are simulated and compared using the presented method. The tooth profile modification was designed based on the simulation results. Moreover, the effects of the tooth profile modification, the sliding friction and the time-varying meshing stiffness upon the dynamic meshing characteristics of continuous engaged gear drives are discussed in detail. The results show that the method is not only effective in designing and evaluating the tooth profile modification, but also in studying the dynamic meshing characteristics of continuous engaged gear drives with realistic time-varying meshing stiffness and tooth sliding friction. The present method could provide an effective tool for vibration mechanism study and dynamic design of the continuous engaged gear drives considering more influence factors.