This paper describes an analytical tool for the design of thin-wall tubes for passage through minimal radius of curvature trajectory. The design is based on a model of thin-wall tube buckling under pure bending. An extended analytical solution for general initial cross section is found based on Brazier method by energy theory of elastic stability. The model predicts the critical moment, curvature, flattening, and stress and allows choosing the most suitable cross section shape for a specific purpose. For example, tubes with ocular and rounded-ocular cross sections were found suitable for semiflexible applications such as endoscopy, where they elastically cross a sharp corner.