The postbuckling behavior of an elastic fiber subjected to lateral constraints is of practical importance in a wide range of medical and engineering applications. The vast majority of existing studies have adopted the assumption that the lateral constrains are fixed in space and rigid. This assumption is often far from the reality of the physical complexity of the abovementioned systems. In this paper, we study analytically, numerically, and experimentally the behavior of an elastic fiber that is subjected to compressive force and constrained by a flexible tube. The latter marks a point of departure from available research. Our experiments provide quantitative information related to the overall behavior of the system, like force-shortening relation and deflection of the flexible tube. That information is complemented by finite-element simulations that enable in-depth analysis of the deformation of the fiber as well as contact characteristics between the fiber and the inner wall of the flexible tube. Finally, a simple mathematical model, aimed at providing analytical insights, is presented. Overall, the theoretical, numerical, and experimental results are in very good agreement. They highlight the fact that the behavior of a compressed fiber that is constrained by a deformable tube significantly deviates from that of a fiber constrained inside a rigid cylinder. Moreover, it is shown that the overall behavior as well as the evolution of contact between the fiber and the cylinder heavily depends on the ratio between the stiffness of the fiber and the lateral stiffness of the tube.