Molecular self-assembly is a powerful technique for developing novel nanostructures by using non-covalent interactions such as hydrogen bonding, hydrophobic, electrostatic, metal–ligand, π–π and van der Waals interactions. These interactions are highly dynamic and are often delicate due to their relatively weak nature. However, a sufficient number of these weak interactions can yield a stable assembly. In this work, we studied the mechanical properties of self-assembled peptide amphiphile nanostructures in the nanometre and micrometre scale. Hydrogen bonding, hydrophobic and electrostatic interactions promote self-assembly of peptide amphiphile molecules into nanofibers. Bundles of nanofibers form a three-dimensional network resulting in gel formation. The effect of the nanofiber network on the mechanical properties of the gels was analyzed by AFM, rheology and CD. Concentration and temperature dependent measurements of gel stiffness suggest that the mechanical properties of the gels are determined by a number of factors including the interfiber interactions and mechanical properties of individual nanofibers. We point out that the divergence in gel stiffness may arise from the difference in strength of interfiber bonds based on an energetic model of elastic rod networks, along with continuum mechanical models of bundles of rods. This finding differs from the results observed with traditional polymeric materials. Understanding the mechanisms behind the viscoelastic properties of the gels formed by self-assembling molecules can lead to development of new materials with controlled stiffness. Tissue engineering applications can especially benefit from these materials, where the mechanical properties of the extracellular matrix are crucial for cell fate determination.