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Pressurized fluid injection into underground rocks occurs in applications like carbon sequestration, hydraulic fracturing, and wastewater disposal, and may lead to human-induced earthquakes and surface uplift. The fluid injection raises the pore pressure within the porous rocks, while deforming them, yet this coupling is not well understood as experimental studies of rocks are usually limited to postmortem inspection and cannot capture the complete deformation process in time and space. We investigate injection-induced deformation of a unique rock-like transparent medium mimicking the deformation of sandstone, yet under low pressure. By incorporating within this artificial rock fluorescent microspheres we capture its internal deformation in real time during the pressurized flow. We then modify the theory of poroelasticity to model accurately and without any fitting parameters the internal elastic deformations, hence providing a physical mechanism for the process. Moreover, our results demonstrate and validate the underling assumptions of the poroelastic theory for fluid injection in rock-like materials. Our results are relevant for understanding human-induced earthquakes and injection induced surface uplift, as they decouple the role of the pressurized flow from the rock deformation through the poroelastic theory.