The present paper proposes a new dynamic failure process simulation model considering the effect of matrix shear failure as well as random fiber breaks based on a shear-lag theory in which an additional time variable is also incorporated by taking the mass of fiber and matrix elements into account. An exact time-dependent stress redistribution process in a composite failure model is evaluated by means of a finite difference scheme based on an increment method for unidirectional carbon (C) and carbon (C) /glass (G) hybrid FRP models. It is observed that the time-dependent stress concentration factor evaluated by the simulation is in good accordance with the Hedgepeth's analytical solution. It is also clarified that the stress in carbon fiber is relieved to some extent due to the presence of neighbouring glass fibers in hybrid C/G hybrid FRP models. The stress wave propagation is successfully simulated by visualizing a time-dependent change in nodal displacements as well as pursuing a dynamic failure process of a composite failure model. These simulations are shown to be effective in characterizing different failure processes and stress wave propagation behaviors of unidirectional CFRP under varied higher strain rates. Finally, a simple damping term is taken into account in the dynamic failure process simulations. It is shown that a clear difference exists in the dynamic failure process and the resulting tensile stress-strain diagram of CFRP and C/G hybrid FRP under varied higher strain rates.