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Terahertz (THz) metamaterials have attracted great attention due to their widely application potential in smart THz devices; however, most of them are fabricated on rigid substrate and thus limit the exploration of flexible THz electronics. In this paper, a flexible THz metamaterial absorber (MMA) incorporated with phase change material vanadium dioxide (VO₂) is proposed. The simulation results indicate that two absorption peaks at around 0.24 THz (marked as A) and 0.46 THz (marked as B) can be observed by designing a I-shaped metamaterial combined with split ring structure. The strong absorption over 92% at 0.24 THz is bending-insensitive, but the absorption at 0.46 THz is bending-sensitive, across the bending angle in the range of 0–50 degrees. Moreover, dynamic modulation of the absorption can be achieved across the insulator-metal phase transition of VO₂. Particularly, the absorption of the A-peak can be tuned from 99.4% to 46.9%, while the absorption of the B-peak can be tuned from 39.6% to 99.3%. This work would provide significance for the design of flexible THz smart devices.