Abstract: In order to control the final pre-tightening force of the stud without measuring rod in the high temperature gas cooled reactor Pebble Module (HTR-PM) and ensure the sealing of the reactor primary circuit pressure boundary, it is necessary to calibrate the pre-tightening force of the stud. Taking the M56 stud without measuring rod as an example, the calibration test was carried out with a bolt tensioner, and the relation curve between the pre-tightening force and the final pre-tightening force of the stud was found. The final pre-tightening force on the stud was smaller than the pre-tightening force of the bolt tensioner when the nut was tightened. The reason of the force decreasing was analyzed. The relation formula between the pre-tightening force and the final pre-tightening force of the stud was established through the constitutive relation theory of material mechanics. It was shown that the final pre-tightening force and its relation between the pre-tightening force obtained from the test were close to the theoretical analysis results. Under the same output force of the bolt tensioner, the final pre-tightening force of the actual equipment nozzle flange studs will be larger than the calibrated value, but this is good for the sealing.