Considering coil stress management, conductor thermal stability, and susceptibility to delamination, the dry-winding approach has been gradually applied and tested in high-temperature-superconducting coils wound with REBa2Cu3O
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(REBCO) coated conductors (CCs). In dry-wound coils, the winding tension can be a useful tool for managing the mechanical stresses and maintaining the structural stability. It is also related to the contact resistivity characteristics of no-insulation and metal-as-insulation coils. In this paper, we present a study on the winding stresses in dry-wound pancake coils considering nonlinear compressive behaviors in the radial direction. Coils wound with stainless-steel (SS) tapes and REBCO CCs were prepared, respectively, with various sizes (90–140 turns) and winding tensions (26–61 MPa). The radial pressure was obtained by applying the pressure measurement films, which cover a pressure range up to 50 MPa. A relatively moderate radial pressure buildup was observed in coils wound with SS tapes, indicating that the effective radial modulus of the coil as an entity is considerably lower compared to the tensile modulus in the azimuthal direction. This is consistent with the nonlinear stress–strain relationship of stacked thin sheets under transverse compression, which can be further explained by the contact behaviors between two rough surfaces. The average radial pressure in CC coils shared similar characteristics as that in SS coils, whereas the radial stress along the conductor edges were significantly higher compared to the middle. Cross-sectional microscopy of the CCs suggests that this can be primarily attributed to the thickness variations across the conductor width. These results suggest that the microscopic rough-surface contact and thickness variation of the wound tape play a critical role in the coil stiffness as well as the winding stress distributions.