In a bolted connection, failures usually initiate at the root of the first bolt thread where the maximum stress occurs. Patterson and Kenney have conducted a comprehensive study for reducing the maximum stress using a 3-dimensional photo-elastic method, and they suggested that a modified nut with straight bevel at the bearing surface was very effective. However, they only dealt with M30 and estimations on the geometry of the modified nut had not been necessarily sufficient. Consequently, it is considered that numerical analyses are needed to determine the optimal shape of the modified nut and to accurately estimate how much the modified nut could reduce the maximum stress for various design factors. In this paper, a numerical approach for multibody contact problem with FEM is proposed by incorporating a regularization method into stiffness matrices to avoid the singularities involved and the validity of the modified nut is investigated as elastic contact problems using the FEM. It is concluded that modified nuts are significantly effective for bolts with large nominal diameter and fine pitch and are practically useful compared with pitch modification and tapered thread methods.