Microtubules (MT) are highly dynamic tubulin polymers that are involved in many cellular processes such as mitosis, intracellular cell organization and vesicular transport. Nevertheless, the modeling of cytoskeleton and MT dynamics based on physical properties is difficult to achieve. Using the Euler-Bernoulli beam theory, we propose to model the rigidity of microtubules on a physical basis using forces, mass and acceleration. In addition, we link microtubules growth and shrinkage to the presence of molecules (e.g. GTP-tubulin) in the cytosol. The overall model enables linking cytosol to microtubules dynamics in a constant state space thus allowing usage of data assimilation techniques.