Abstract: In this paper, conformal mapping is employed to study the stress concentration on thin cylindrical shells with large non-circular openings. Based on the theoretical solutions of thin cylindrical shells with large openings, the mapping functions are obtained for non-circular and non-elliptical cutouts. Numerical results for free elliptic cutouts with different opening ratios and different external loading conditions are obtained and compared with available solutions based on small opening theory. It is shown that the solutions of stress concentration based on large opening theory are more reasonable.