In the present study, the collapse behavior of RTPs was analyzed by an experimentally-verified numerical method, in which the eccentricity directions, the combinations of eccentricity and initial ovality are considered. Eigenvalue analysis and Riks analysis were combined to simulate the progressive failure of composites during the collapse, which was conducted by a continuum damage model based on Hashin failure criterion and fracture energy dissipation. The stress analysis showed that the hoop stress of composites is much higher than that of isotropic layers both in the elastic and progressive failure phases. Because of this, thick composites always play important roles in bearing external pressure. Except the experimentally observed O-/U-type collapse modes, the C-type collapse mode was observed and simulated for the first time. They all go through the uniform contraction-collapse-large deformation process, and have the same failure modes of composites. However, different from the O-/U-type collapse modes, the cross-sectional deformation of the C-type collapse is not symmetrical and has a moving maximum-displacement point. The collapse pressure decreases linearly as the increase of the eccentricity and the initial ovality. The effect of eccentricity directions can be concluded as: more dispersed eccentricity distribution makes composites contribute more to the pressure resistance.