There is no analytical solution to the stress, strain and displacement changes in the inner sleeve of the downhole packer during service. In this paper, the inner sleeve structure is simplified based on the shell theory model, and the geometric equation and physical equation suitable for the inner-sleeve structure are established based on the control differential equation of the cylindrical shell derived by Flügge. Finally, the analytical solution calculation program of the radial displacement, and strain and stress value of each node of the cylindrical shell under the external load condition is compiled by using MATLAB R2024a software. The analytical solution is compared with the numerical solution of each parameter under the same conditions, and the root mean square error between the numerical solution and the analytical solution is evaluated. The results show that the analytical formulas of the stress, strain and displacement of the inner sleeve structure of the downhole packer established in this paper can accurately obtain the above parameters. The root mean square errors between the analytical formulas and the numerical solutions are 0.083, 0.074 and 0.086, indicating that the fitting degree between the two is good, which verifies the effectiveness of the theoretical model based on the shell to describe the stress state of the inner sleeve. The model also accurately reflects the partial stress and strain law of the inner sleeve of the downhole packer to a certain extent. This study provides theoretical support for the design optimization of the inner sleeve of a pipeline packer, and also provides some guidance for the study of the stress state of its inner sleeve.