The dependence of the local Young's modulus of organic thin films on the size of the domains at the nanometer scale is systematically investigated. Using atomic force microscopy (AFM) based imaging and lithography, nanostructures with designed size, shape, and functionality are preengineered, e.g., nanostructures of octadecanethiols inlaid in decanethiol self-assembled monolayers (SAMs). These nanostructures are characterized using AFM, followed by force modulation spectroscopy and microscopy measurements. Young's modulus is then extracted from these measurements using a continuum mechanics model. The apparent Young's modulus is found to decrease nonlinearly with the decreasing size of these nanostructures. This systematic study presents conclusive evidence of the size dependence of elasticity in the nanoregime. The approach utilized may be applied to study the size-dependent behavior of various materials and other mechanical properties.