Abstract: During drilling job, BHA failures take place frequently, which concentrate on the thread connection. So decreasing of the stress concentration on connection becomes very important. Machining stress-relief grooves on thread in order to decreasing the stress concentration is brought forward by researchers at home and abroad, which has excellent effect. Take pin threads of ?177.8 mm drill collar for instance, Finite Element Method is used to analyze the different stress-relief grooves of pin thread connection, so the stress concentration on the last engaged pin threads is gained. FEM Results showed that stress of the pin threads with stress-relief grooves is smaller than that of API standard connection without stress-relief grooves and the stress-relief grooves of API standard is best for resistance of fatigue.