Using atomic force microscopy we have studied the nanomechanical response to nanoindentations of surfaces of highly oriented molecular organic thin films (thickness⩽1000 nm). The Young’s modulus E can be estimated from the elastic deformation using Hertzian mechanics. For the quasi-one-dimensional metal tetrathiafulvalene tetracyanoquinodimethane E∼20 GPa and for the α phase of the p-nitrophenyl nitronyl nitroxide radical E∼2 GPa. Above a few GPa, the surfaces deform plastically as evidenced by discrete discontinuities in the indentation curves associated to molecular layers being expelled by the penetrating tip.