The problem of finding the optimum ratio between the wall thickness of the metal hull of a cylindrical pressure vessel and the thickness of its reinforcing fiber jacket is solved. The random nature of the material’s mechanical and strength properties and the loading conditions are taken into account in evaluating the strength of the structure. Early stages in deterioration of the material are predicted from a model microinhomogeneous medium for stochastic granular and fiber composites. The distribution laws of the microstructural stresses and strength conditions are calculated and used to find the probability of failure of the material at the most critical points for various strength-margin factors. A numerical example is given for a closed cylinder with a VT-6 alloy hull and a reinforcing jacket of Armos fibers.