Post-tensioned tanks for nuclear and energy storage applications are small radius cylindrical concrete structures in most cases. A large pre-compression force must be applied to withstand the high levels of tension produced by both the inner pressure and the temperature gradient between the inner and outer faces of the wall (regardless of the inhomogeneous material alteration due to the latter). Hence, high curvature horizontal (circumferential) tendons with a large number of strands, heavily post-tensioned, must be placed with the smallest possible vertical separation. The resultant radial post-tensioning force is transmitted to the net concrete section through its interface with the duct. The strands however pile up pushing inside the duct producing vertical pressure components along an arc, as well as the flattening out of the duct. The duct detaches then of the concrete leading to a crack initiation. This study presents a strongly non-linear model that attempts to account for all these factors. The results show that the concrete-duct contact must be modeled in order to prevent a crack sewing effect that may greatly overestimate the section capacity to withstand the post-tensioning, not to say the service mechanical and thermal loads. It also shows that these structures require higher tensile concrete strengths, and Ultra High Performance Concrete and Ultra High Performance Fiber Reinforced Concrete must be considered in order to make these tanks viable.