This paper especially highlights the finding that the mechanical properties of polymeric nanofibers can be tuned by changing the fiber size as well as the composition. For this purpose, the bending Young's modulus was determined using atomic force microscope by involving single-material (polyvinyl alcohol (PVA), polyethylene oxide (PEO 400K)) and composite nanofibers (polyvinyl alcohol/hyaluronic acid (PVA/HA), polyethylene oxide/chitosan (PEO 400K/CS)). The mechanical property, namely the bending Young's modulus, increases as the diameter of the fibers decreases from the bulk down to the nanometer regime (less than 200 nm). The ranking of increasing stiffness according to the AFM measurements of the three-point beam bending test are in agreement, and can be ranked: PEO 400K < PVA/HA ≈ PVA < PEO < 400K/CS. According to our results, CS-based nanofibers are the stiffest (15 GPa) and the most resilient to erosion in an aqueous medium. Consequently, they possess the most appropriate attributes for bone, tendon, and cartilage tissue scaffold engineering. Nanofibers based on PVA (6 GPa) and PEO (3 GPa) are more elastic (a smaller bending Young's modulus) and therefore are the most suitable for skin and wound tissue scaffolds.