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• Exact analytical solutions of stress distributions in a hollow cylinder under contact interactions are established. • Governing equations are analytically uncoupled by introducing displacement functions. • Hertz contact is re-written as Fourier series to create a versatile description of contact interactions. • Effects of design parameters on stress fields are comprehensively discussed. • Novel maximum normalized stress maps are created for stress distribution mechanism analysis. Bundled hollow cylinders are extensively found in natural materials and engineering structures. Aiming at a theoretical basis of structural rigidity and integrity, the present study provides exact analytical solutions of stress distribution within a hollow cylinder under contact tractions by the neighbors in one-dimensional chains. Displacement functions are introduced to uncouple the governing equations, and explicit expressions of stress components are obtained. Hertz contact at the interaction surface is considered and re-written by Fourier series to determine the unknown coefficients. Traits of stress distribution within the hollow cylinder are addressed and significant non-uniformity is indicated along both the radius and circumference. Parameter studies are conducted to investigate the effects of material and geometry on the stress distribution. Furthermore, novel maximum normalized stress maps are developed, providing an effective approach to understand stress distribution mechanisms. The ultimate stress transits from the circumferential compressive type to the radial compressive type with the increasing thickness-diameter ratio. If excluding compressive stresses, the hoop tensile and the in-plane shear types are predominant for different thickness-diameter ratios, respectively. The present investigation should help to understand the failure mechanisms and can be utilized to create a versatile method of engineering materials constructed by bundled hollow cylinders. [Display omitted] [ABSTRACT FROM AUTHOR]