Abstract: A representative volume element (RVE) taking account of the contact and jamming of yarns, coupled with the periodical boundary condition was chosen to simulate the progressive damage behavior of 3D braided composites. The tensile strengths were predicted from the calculated stress-strain curves. The stiffness matrix of the damaged material was established by the method of introducing damage variables to the strain energy density function. The damage evolvement method by introducing damage variables of different damage modes were considered as the progressive damage of the material integral points. Hashin and Tsai-Wu failure criterions were adopted to identify damage initiation of the braiding yarns. They were analyzed and discussed by comparing numerical predictions with two typical specimens’ experimental data. The results indicate that numerical simulation based on Tsai-Wu failure criteria with various damage modes gives good agreement compared to experimental results, Hashin criteria is not suitable for predicting the occurring of damage of braiding yarns. Specimens with different braided angles show different damage mechanisms.