Thin-film transistors (TFTs) fabricated on flexible plastic substrates are an integral part of future flexible large-area electronic devices like displays and smart textiles. Devices for such applications require stable electrical performance under electrical stress and also during applied mechanical stress induced by bending of the flexible substrate. Mechanical stress can be tensile or compressive strain depending on whether the TFT is located outside or inside of the bending plane. Especially the impact of compressive bending on TFT performance is hard to measure, because the device is covered with the substrate in this case. We present a method which allows us to continuously measure the electrical performance parameters of amorphous Indium-Gallium-Zinc Oxide (a-IGZO) based TFTs exposed to arbitrary compressive and tensile bending radii. To measure the influence of strain on a TFT it is attached and electrically connected to a flexible carrier foil, which afterwards is fastened to two plates in our bending tester. The bending radius can be adjusted by changing the distance between these plates. Thus it is possible to apply bending radii in the range between a totally flat substrate and ≈1 mm, corresponding to a strain of ≈3.5%. The tested bottom-gate TFTs are especially designed for use with our bending tester and fabricated on 50 μm thick flexible Kapton® E polyimide substrates. To show the different application areas of our bending method we characterized our TFTs while they are bent to different tensile and compressive bending radii. These measurements show that the field effect mobilities and threshold voltages of the tested a-IGZO TFTs are nearly, but not absolutely, stable under applied strain, compared to the initial values the mobilities shift by ≈3.5% in the tensile case and ≈−1.5% in the compressive one, at a bending radius of 8 mm. We also measured the influence of repeated bending (2500 cycles over ≈70 h), where a shift of the performance parameters can be observed, too. The saturation mobility of the flat device decreases by 4.5%, and the threshold voltage raises 0.1 V. These results show that it is possible to characterize the influence of different kinds of bending on flexible thin-film devices in a very reliable way with one experimental setup.