The severe dynamic environment of take-off and flight of launchers presents risks of damage and life cycle limitation of the payload. To improve the dynamic comfort of the payload, damping treatments are employed at the final stage of the launcher assemble. One well-known solution is the limitation of the vibration amplitudes by dissipating the energy at the bolted joints between the stages. To our knowledge, there is not a simple and effective method that allows an accurate damping prediction at the full structure level from the knowledge of localized dissipation between the components. Indeed, to model the damping of an assembled structure made up of several components, one carries out a 3D modeling of the interfaces [1] to have a good representation of the dissipation. The result is a damping model identified by interface, which is difficult to exploit in the prediction of the dynamic behavior of the full model. Moreover, for uniformly distributed dissipation, it is common to use the Rayleigh damping assumption to represent the damping matrix in the equivalent viscous model. In general, common methods [2] identify this matrix at a single interface. In this work, we propose a method of modeling the multi-interface Rayleigh damping which consists of the following steps: (i) calculation of the modal damping of each interface taken separately by using the modal effort method [3] or the modal displacement method developed in PERMAS finite element software; (ii) identification of the proportional damping matrix of each interface (proportionality coefficients of stiffness and mass matrices); (iii) assembly of the identified damping matrices; (iv) prediction of the dynamic response of the complete structure from the global model. The proposed method was validated on a reduced model of the ARIANE 5 launcher to calculate the dynamic responses taking into account the different types of dissipation in the interfaces for the asymmetric load case and successfully compared to the reference results. The main advantages of the proposed method are the simplicity of the numerical implementation, the reduction of the CPU, the quality of prediction and the perspective of integration in an optimization procedure of interfaces design with high damping performances.