We demonstrate a lithography-free approach to create a crystalline Si nanomembrane (NM) on a flexible polydimethylsiloxane (PDMS) substrate, and to induce uniaxially tensile strain in the Si NM by mechanically stretching its host PDMS substrate. We start from a commercial silicon-on-insulator (SOI) wafer, remove the buried oxide (BOX) layer using hydrofluoric acid (HF), and transfer the weakly bonded Si NM onto a PDMS substrate by stamping. Flat and smooth Si NMs are created on PDMS substrates by this method, and the typical area of each crack-free region is larger than 100 μm × 100 μm. The root mean square (RMS) roughness of the crack-free regions of a transferred Si NM, as determined by atomic force microscopy (AFM), is typically 0.4–0.5 nm. Using x-ray diffraction (XRD) characterization, we confirm that the Si NM transferred on a PDMS substrate exhibits high crystalline quality that is compatible for device fabrication. We introduce tensile strain in the Si NM by stretching the PDMS substrate where the Si NM is hosted using a home-made mechanical tool. Raman spectroscopy analysis reveals that uniaxial tensile strain up to 1.0% is introduced along the <110> direction of the Si(001) NM. This work suggests that Si NMs created by this lithography-free approach are promising for applications in electronics and optoelectronics.