Novel applications for memory devices demand nanoscale flexible structures. In particular, resistive switching (RS) devices are promising candidates for wearable and implantable technologies. Here, the Pt/Si/Ag/TiW metal-insulator-metal structure was fabricated and characterized on top of flexible substrates using a straightforward microfabrication process. We also showed that these substrates are compatible with sputtering deposition. RS was successfully achieved using both commercial cellulose cleanroom paper and bacterial cellulose, and polymer (PET) substrates. The bipolar switching behavior was observed for both flat and bent (under a radius of 3.5 mm) configurations. The observed phenomenon was explained by the formation/rupture of metallic Ag filaments in the otherwise insulating Si host layer.