A flat steel ribbon wound pressure vessel was adopted by ASME Code Case 2229 on 16 August 1996. By considering the additional strength caused by friction between ribbon layers, the authors deduced equations for prediction of longitudinal and hoop bursting pressure of such vessels. The calculation results from the equations, which are easy to calculate and convenient to apply in the engineering, are in excellent agreement with experimental results. It is the theoretical base for equal strength design in axial and circumferential direction. In addition, the criterion of failure form of such a vessel is also given.