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Galling is one of the most familiar failure forms for tubing and casing connections. It has been regarded as a key problem by metallurgy and petroleum systems all over the world. The theory of tribology and contact mechanics was used to analyze the contact force, plastic strain, and other parameters of API 10-round tubing connections in the process of makeup and breakout using the nonlinear finite element method. The stress states of the tubing thread connections were also analyzed for combined makeup and axial tensile loads. The results show that the main factors for tubing thread galling failure with thread grease are the normal contact force of the pin and box and the rigidity of the thread surface. The distribution of the contact force can be improved and the high contact force of the local thread can be reduced by optimizing the geometric parameters of the thread or using a small or varied pitch. The thread surface rigidity can be increased by improving the thread surface machining quality and by heat treatment. The chance of tubing thread galling failure can be reduced by designing hydraulic pressure tongs to avoid high speed and high torque makeup and by standardizing the operations of oilfield makeup and breakout.