Safe separation of the rocket payload fairing is one of the most important factors that affect the success of a flight mission. In recent years, composite materials instead of aluminum alloys are widely used in rocketry. Such materials must satisfy a number of requirements that include the certainty of a local failure due to the action of a cumulative charge of the given power. To analyze this process numerical research is an advisable approach. The model of a composite rocket fairing separating due to the action of a cumulative charge has been developed. The properties of the composite material have been modeled based on the averaged characteristics obtained experimentally. The cumulative charge has been modeled by impulse loading having parameters adequate to the charge type. The time of action of the impulse, maximum pressure and width of the loading area are determined from the charge properties and geometry. The rocket fairing is considered as a composite shell composed of conical and cylindrical parts. A technique for 3D numerical analysis of the dynamic strength and structural failure has been developed. The mathematical model of the structure deformation and failure takes into account the dynamical properties of the material. The maximum plastic deformation is used as a failure criterion. The results of numerical simulation for the typical rocket payload fairing are presented.