Freestanding carbon nanomembranes (CNMs) with a thickness between 0.6 and 1.7 nm were prepared from self-assembled monolayers (SAMs) of diverse polyaromatic precursors via low-energy electron-induced cross-linking. The mechanical properties of CNMs were investigated using AFM bulge test, where a pressure difference was applied to the membrane and the resulting deflection was measured by atomic force microscopy. We found a correlation between the rigidity of the precursor molecules and the macroscopic mechanical stiffness of CNMs. While CNMs from rigid and condensed precursors like naphthalene and pyrene thiols prove to exhibit higher Young's moduli of 15-19 GPa, CNMs from nonfused oligophenyls possess lower Young's moduli of similar to 10 GPa. For CNMs from less densely packed SAMs, the presence of defects and nanopores plays an important role in determining their mechanical properties. The finite element method (FEM) was applied to examine the deformation profiles and simulate the pressure-deflection relationships.