To ensure both adequate axial load-bearing capacity and radial vulnerability of a circumferentially notched thin cylindrical shell is one of the major challenges in designing some crucial aerospace structures such as the pyrotechnic separation devices. The most favorable design for such a shell is to optimize the notch geometry such that zero stress at the notch root is realized, which enhances the axial strength without impacting the notch failure during separation. However, few studies have focused on such extreme stress concentration-free designs of a single-side notch on a shell because the asymmetrical structure under common eccentric loading brings much difficulty for theoretical analysis, while numerical approaches can hardly meet the requirements of highly efficient rapid optimal designs. In this paper, a theoretical and experimental study toward extreme stress concentration-free designs of single-side-notched thin cylindrical shells is presented. The general stress concentration factors (SCFs) for single-side notches with arbitrary depths are obtained based on the theory of notch stresses, which are well validated by the refined finite element modeling. An important finding reveals that, for a common notched shell in aerospace vehicles, the stress at the notch root approaches zero when a specific ratio of load eccentricity to minimum section width is attained. Comprehensive experiments for specially designed notched specimens confirm the theoretical finding. The present study provides an effective approach to analyzing single-side-notched structures and yields an explicit quantitative guideline for the optimal design of circumferentially notched thin cylindrical shells.