The surface stresses in band reinforced cylindrical pressure vessels are examined, and an equivalent stress determined by using the Mises- Hencky criterion. By comparing the equivalent stress to the band stress, the efficiency of the structural material can be established, and by equating these stresses to their respective yield stresses, the theoretical maximum strength of the structure can be found. Once the material properties of the shell and the reinforcing bands have been specified, the optimum structural layout can be determined.