Abstract: Ribbon or wire prestressed cylinder for high pressure vessels or cold extrusion dies consists of two parts: the winding and core. Winding with constant shear stress most efficiently utilizes winding materials and permits maximum possible internal working pressure. It is desired that under working pressure there is no tensile hoop stress at the inner face of the core in order to prevent from early cracking and increase fatigue strength. In this paper, method of optimum design and calculation equations are derived for this purpose.