In order to verify the delamination damage occurring in thick-walled composite-overwrapped pressure vessels, firstly, for composite delamination damage, a composite laminate model was established. Model I and model II delamination failure processes of composite structures were simulated and verified based on a tiebreak contact algorithm for different mesh sizes, respectively, and the approximate equivalent results were achieved by correcting the inter-ply strength. Then, for in-plane damage to composite materials, the elastic–plastic process was verified by selecting a progressive damage model, with quasistatic nonlinear tensile shear of sample specimens as an example. Further, under the purpose of generality and simplicity, the location of the first occurrence of delamination failure was simulated and analyzed with the tiebreak contact algorithm and a reasonable mesh size, using quasistatic loading of a thick composite-overwrapped pressure vessel cylindrical section as an example. The results showed that delamination occurred at approximately the center, which is in general agreement with the experimentally observed phenomenon. On this basis, the locations of the first significant delamination phenomena in composite-overwrapped vessels under three different ratios of plus or minus 45-degree layup angles were predicted. Finally, the differences in structural strength between the single laying methods and the combined laying method were compared. The results showed that the ratio of 50% had a higher modulus value than a pure 0° ply, but too large a ratio was detrimental to the improvement of structural properties.