Microtubule polymer is one of the most abundant proteins in the body and one of the three main components of the cell framework. This protein has the task of bearing the mechanical loads on the cell and providing the necessary force to alter the cell proliferation, cell migration, and cell division. Also, microtubule plays a key role in intracellular traort. Therefore, studying the behavior and mechanical properties of microtubule is an important issue, which has attracted the attention of many laboratory studies and computer modelings. In this research, the study of mechanical and vibrational properties of microtubules is investigated, to do this, molecular dynamics simulation is used and the research developped using modified techniques based on continuous mechanics. The first step of this research includes computer simulations and extracting mechanical and vibrational properties related to the modeling dimensions. Because there are a large number of atoms in the studied system, the way to do all-atom modeling has many difficulties and is time consuming, the coarse-grained modeling. Is attended. Acceptable results of coarse-grained modelings in many researches provide a promising prospect into the effects of coarse-grained models in future molecular simulations, which is expected to be extended to other biomechanical examples with a large number of atoms. It made it possible to study the large systems in terms of nanoscale and reveal their quantitative and qualitative features and determine how their substructures behave in atomic dimensions. In the following, using mathematical modeling and applying the modified continuous mechanics theory for the nanostructure, the constitutive equations are derived and solving them using numerical solutions are considered. By making nonlocal parameter non-dimensional and optimizing it using the molecular dynamic simulations results, the vibrational behavior of microtubule for various lengths and parameters is investigated. At the end of this study, proximity of the results, pertaining to the mechinical properties of this research to those of previous studies shows the accuracy of modelings and simulations. Keywords: Molecular Dynamic Simulation, Differential Quadratic Method, Nanobiomechanics, Cell Mechanics, Cellular Microtubule, Finite Element Method, Nonlocal Theory