Abstract: According to the theory of elastic contact, the artical, using finite element mixing method, analyses contact stress in the thread pipe connection. Examples are given and contact stresses calculated. Calculations show that the greatest stress of flange concentrates on the first thread root of the upper end, and that of pipe falls on the third root beyond where pipe contacts flange, and a minimum zone comes into yield condition. The article provides theoretical basis for stress checking of pipe flange thread, design of structures and analysis on seals properties.