The elastic properties of the nanotubes of self-assembled aromatic dipeptide diphenylalanine are investigated by means of Raman spectroscopy and a mass-in-mass 1D model. Analysis of nanotubes' lattice vibrations reveals the essential contribution of the water in the nanochannel core of the tubes to the Young's modulus and high water mobility along the channel. Direct measurements of the Young's modulus performed by nanoindentation confirm the obtained results.