The giant magnetoimpedance effect of multilayered thin films under stress has great application prospects in magnetic sensing, but related studies are rarely reported. Therefore, the giant magnetoimpedance effects in multilayered thin film meanders under different stresses were thoroughly investigated. Firstly, multilayered FeNi/Cu/FeNi thin film meanders with the same thickness were manufactured on polyimide (PI) and polyester (PET) substrates by DC magnetron sputtering and MEMS technology. The characterization of meanders was analyzed by SEM, AFM, XRD, and VSM. The results show that multilayered thin film meanders on flexible substrates also have the advantages of good density, high crystallinity, and excellent soft magnetic properties. Then, we observed the giant magnetoimpedance effect under tensile and compressive stresses. The results show that the application of longitudinal compressive stress increases the transverse anisotropy and enhances the GMI effect of multilayered thin film meanders, while the application of longitudinal tensile stress yields the opposite result. The results provide novel solutions for the fabrication of more stable and flexible giant magnetoimpedance sensors, as well as for the development of stress sensors.