A flange, which is integrally formed with the inner surface of the cylindrical member, is located at an intermediate point between the end surface position of the cylindrical member to which the electrode plate of one of the discharge electrodes is sealed and the tip position of the discharge electrode portion of that electrode. Both end surfaces of the cylindrical member are hermetically attached with the discharge electrodes. This arrangement prevents inner flashovers without affecting the discharge characteristics of the discharge tube and also ensures manufacture of discharge tubes with no possibility of gas leakage with very high yields even if the machining precision is not so high.