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Topologically interlocking material (TIM) systems are composed of convex polyhedral units placed such that building blocks restrict each other’s movement. Here, TIM tubes are considered as rolled monolayers of such assemblies. The deformation response of these assembled tubes under diametrical loading is considered. This investigation employs experiments on additively manufactured physical realizations and finite element analysis with contact interactions. The internal load transfer in topologically interlocking tubes is rationalized through inspection of the distribution of minimum principal stress. A thrust-line (TL) model for the deformation of topologically interlocking tubes is established. The model approximates the deformation behavior of the assembled tubes as the response of a collection of Mises trusses aligned with paths of maximum load transfer in the system. The predictions obtained with the TL-model are in good agreement with results of finite element models. Accounting for sliding between building blocks in the TL-model yields a predicted response more similar to experimental results with additively manufactured tubes.