Small snubber of hydrogen compressor do duty as buffer pulsation of compressed hydrogen. Snubber is a kind of internal pressure vessel and design optimum of snubber very important problem. In this paper, we will estimation results of elastic finite element structural analysis using the commercial program such as ANSYS for comparison to the limits in ASME Code Sec. Ⅷ that are related to membrane and bending stresses. In case of membrane stress in a circular cylindrical due to internal pressure or to distributed live loads. Bending stress in the central portion of flat head due to pressure. In addition, We will propose optimum design value of snubber for hydrogen compressor.