High stress concentrations are produced near the flange connection of thin-walled pipes subjected to high internal pressure and under high temperature, because the rigidity of flanges is generally much larger than circular pipes. To give the information of the stress concentrations, stress distributions near the flange connection were obtained elastically, and relations between the stress concentrations and the rigidity of flanges were theoritically determined by using a "Coefficient of Constraint of flange" which depends on shape and dimensions of flanges and pipes. Near the flange connections axial tensile stress is much larger than hoop tension, and the concentration of axial stress gradually increases as the increase of the coefficient of constraint of flange. To verify the theories, deformations of model pipe as shown in fig. 3 under internal hydraulic pressure were measured experimentally by electric wire strain meter, and stresses were calculated by the data. From the results, it was found that the theoritically calculated stress values and experimentally obtained ones show fairly good coincidence.