Pressurized shells with an obround cross-section are common components in the petrochemical industry. However, the analysis and design of obround components have been challenging due to their complex shapes. Empirical and numerical methods are commonly used for their analysis and design. In this study, the obround shape is divided into curved and straight segments to simplify the geometry and boundary conditions within each segment. The theoretical analysis of each segment was performed separately. By combining existing closed-form solutions, a theoretical solution was developed that partially satisfies the deformation at the junction of segments. This combined solution can accurately calculate stress and displacement in obround shells under internal pressure, representing a closed-form theoretical solution for pressurized obround shells. When the length of the straight segments approaches zero, the obround shell becomes cylinder, the proposed solution returns to the solution of cylindrical shell or Lame’s solution. The solution provides a new theoretical analysis approach that is simpler, more efficient, and more accurate than empirical methods or numerical analyses. It is expected to change the current reliance on empirical formulas and numerical simulations for analyzing obround components and to promote the development of a new design methodology for obround components.