A comparative investigation of preconditions for cracking in thick-walled anisotropic unidirectionally and cross-ply filament-wound cylinders was performed. Experiments showed that it was much more difficult to obtain monolithic (without hoop cracks) thick cross-ply filament-wound cylinders than thick unidirectionally filament-wound cylinders. During cooling, cracks in cross-ply cylinders with a smaller ratio of thickness to the inner radius (at/of about 10% compared with 60% for unidirectionally filament-wound ones) are generally formed. However, the calculations of thermal stresses, by two different models, in a continuous anisotropic medium and in rings consisting of n alternating glass and resin layers showed that the radial tensile stresses in thick cross-ply filament-wound cylinders were lower than in a unidirectional structure. Only calculations by the FEM demonstrated higher radial tensile stresses in the cross-ply structure.