The setting performance of a packer is directly affected by the anchoring effect of a packer slip on the casing. When the slip is embedded into the casing, bite marks can be formed on the casing contact surface, and excessive embedded depth may lead to casing damage and failure. To ensure that slips perform a good packer fixing function while reducing the damage to the casing, this paper adopted the slip line theory, finite element analysis method and experimental method to study the mechanical behavior of slips in the process of anchoring and calculated the embedded depth of the slip in the casing. In addition, influences of slip thread angle, inclination angle, inner cone angle and axial load on the anchoring were analyzed, and structural parameters were optimized. And the following research results were obtained. First, the stress distribution on the casing contact surface is uneven, which results in stress concentration. Second, the stress of slip tooth decreases gradually as the number of teeth increases. Third, the embedded depth of the slip tooth in the casing increases with the increase of load, but decreases gradually with the increase of the number of teeth. Fourth, under the same load, the embedded depth of the slip in the casing decreases with the increase of thread angle and inner cone angle, but increases with the increase of inclination angle. Fifth, slip anchoring and packer setting experiment under high temperature and high pressure shows that the maximum embedded depth of the slip in the casing is between 0.40 mm and 0.45 mm. In conclusion, experimental results and finite element simulation results are better consistent, which verifies the correctness and reliability of the design and analysis.