Foam-filled tubes represent one of the best energy-absorbing components for future crashworthiness applications. Triply Periodic Minimal Surface (TPMS)-filled tubes were investigated under quasi-static and dynamic three-point bending loading conditions. The TPMS-filled tubes enhanced specific energy absorption up to 46% compared to the sum of empty tubes and the core response separately. The validated computational models were used to extend the computational study to investigate graded core of TPMS-filled tubes under bending loading. The study results show that the mechanical response of TPMS-filled tubes can be tuned using different relative densities or/and distributions of relative density of the core.