Based on the first, third, and fourth strength theories, this paper deduces the strength checking calculation formula of the thick-walled cylinder under different strength theories. The three strength checking methods are compared and analyzed in three aspects of calculating wall thickness, maximum allowable calculated pressure and reduced internal pressure stress, and it is concluded that the calculation formulas of the three strength checking methods are inconsistent and the calculation results are biased. And then, the influence of the K value on the strength checking results and the change of allowable stress with the strength characteristics of materials are also discussed. Finally, FEA technology demonstrates that the maximum peak stress obtained from the thick wall theory is inaccurate, and the stress redistribution caused by creep relaxation should be considered.