In order to reduce the failure accidents caused by the insufficient strength of fracturing string joints, theoretical calculation and string design methods were adopted to conduct finite element calculations on commonly used long circular threads. The distribution laws of stress and contact pressure of long round threads were obtained, a non-standard special thread was designed, and a finite element model of the joint of the casing was established. Considering different make-up torques, tensile loads, and tensile torque loads within a certain range, the stress variation law of the special casing threaded joint under this design size was analyzed. Finally, the stress and contact pressure variation law on the threaded tooth was analyzed under different structures, working conditions, and wall thickness parameters. The thread strength and sealing function were compared under various parameters. The results showed that the smaller the wall thickness of the joints, the greater the contact pressure at the threaded tooth. Among them, the contact pressure of the external threaded tooth is too high, and is prone to the sticking phenomenon. The distribution of contact pressure in the middle section is relatively reasonable. Compared with the original structure, the new structure significantly reduces the contact pressure at the head and tail ends of the threaded connection, reducing the risk of sticking.