Vibration of drillstring is the most important factor of its destruction and reduction in drilling operations efficiency. One of the main causes of excessive vibration of drillstring is drillstring-wellbore contact, therefore drillstring-wellbore contact has been studied in several researches. Indeed the contact behavior of drillstring and wellbore is of great concern to drilling companies in the oil and gas exploration industries. In this research, dynamic behavior and vibration of non-linear finite element model of a drillstring in contact with wellbore, has been investigated. By considering total length of drillstring, a three-dimensional timoshenko beam element is employed. In addition the geometric stiffening effect including nonlinear terms, the added fluid mass and the contact between drillstring and borehole wall has been considered using improved contact model with a more complete model than previous studies, that the stiffeness of contact determined form energy balance relations. The equation of motion of drillstring obtained using energy approach and lagrange’s equations and full order equations are used to drive the results. Coupling between various vibrations has been tested and the effect of recent model in analysis of dynamic behavior and vibration of drillstring have been evaluated.