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Future flexible electronic systems require memory devices combining low-power operation and mechanical bendability. Here, we present mechanically flexible amorphous InGaZnO (a-IGZO) memory thin-film transistors (TFTs) with a ferroelectric poly(vinylidene fluoride-trifluoroethylene) [P(VDF-TrFE)] gate insulator. Memory operation is demonstrated with a memory window of 3.2 V and a memory ON/OFF ratio of 1.5×106 (gate-source voltage sweep of ±6 V). The measured mobility of 8 cm2 V-1s-1 and the ON/OFF current ratio of 107 are comparable with the values for reference TFTs fabricated on the same substrate. To use memory TFTs in flexible applications, it is crucial to understand their behavior under mechanical strain. Flexible memory and reference TFTs are characterized under bending radii down to 5.5 mm, corresponding to tensile and compressive strain of ≈ ±0.6%. For both memory and reference TFTs, tensile strain causes negative threshold voltage shifts and increased drain currents, whereas compressive strain results in the opposite effects. However, memory TFTs, compared with reference TFTs, exhibit up to 8× larger threshold voltage shifts and 17× larger drain current variations. It is shown that the strain-dependent properties of a-IGZO can only explain the shifts observed in reference TFTs, whereas the variations in memory TFTs are mainly caused by the piezoelectric properties of P(VDF-TrFE).