Nanostructured FeNi-based multilayers are very suitable for use as magnetic sensors using the giant magneto-impedance effect. New fields of application can be opened with these materials deposited onto flexible substrates. In this work, we compare the performance of samples prepared onto a rigid glass substrate and onto a cyclo olefin copolymer flexible one. Although a significant reduction of the field sensitivity is found due to the increased effect of the stresses generated during preparation, the results are still satisfactory for use as magnetic field sensors in special applications. Moreover, we take advantage of the flexible nature of the substrate to evaluate the pressure dependence of the giant magneto-impedance effect. Sensitivities up to 1 Ω/Pa are found for pressures in the range of 0 to 1 Pa, demostrating the suitability of these nanostructured materials deposited onto flexible substrates to build sensitive pressure sensors.