This paper presents design safety analysis of pressure vessels. The gas pressure and thermal loads are applied to the pressure vessel simultaneously. In this study, ASME Sec. VIII Div. 2 code was accepted for the safety design of high-pressure vessel. And this result was analyzed using a coupled thermal-mechanical FEM analysis technique. The FEM computed result shows that ASME design code may not guarantee for combined loads of high gas pressure and thermal loads. And solid pressure vessel may be safe compared to other pressure vessels with supporting rings round the cylinder body.