The basic unit in microtubules is alphabeta-tubulin, a heterodimer consisting of an alpha- and a beta-tubulin monomer. The mechanical characteristics of the dimer as well as of the individual monomers may be used to obtain new insight into the microtubule tensile properties. In the present work, we evaluate the elastic constants of each monomer and the interaction force between them by means of molecular dynamics simulations. Molecular models of alpha-, beta-, and alphabeta-tubulins were developed starting from the 1TUB.pdb structure from the RCSB database. Simulations were carried out in a solvated environment by using explicit water molecules. In order to measure the monomers' elastic constants, simulations were performed by mimicking experiments carried out with atomic force microscopy. A different approach was used to determine the interaction force between the alpha- and beta-monomers by using 16 different monomer configurations based on different intermonomer distances. The obtained results show an elastic constant value for alpha-tubulin of 3.8-3.9 Nm, while for the beta-tubulin, the elastic constant was measured to be 3.3-3.6 Nm. The maximum interaction force between the monomers was estimated to be 11.9 nN. A mechanical model of the tubulin dimer was then constructed and, using the results from MD simulations, Young's modulus was estimated to be 0.6 GPa. A fine agreement with Young's modulus values from literature (0.1-2.5 GPa) is found, thus validating this approach for obtaining molecular scale mechanical characteristics. In perspective, these outcomes will allow exchanging atomic level description with key mechanical features enabling microtubule characterization by continuum mechanics approach.