In the present work a continuous model is presented to study, by means of finite element discretization, the coupling of extensional, flexural and torsional vibrations under a state of initial stresses on a drillstring, which is described as a vertical slender beam under axial rotation [
]. The structure is subjected to distributed loads due to its own weight, the reaction force and perturbation moments at the lower end. The beam structure is also confined to a move inside a rigid cylinder, which simulates the borehole [
]. The impacts and friction of the drill-string with the borehole are modeled employing simplified forms. It is known that the state of initial stresses (which implies accounting for geometrical non-linearities) affects the dynamics of slender beams. The vibrations of drill-strings are frequently analyzed by means of lumped parameter models [
]. Normally, these models employ equivalent lumped parameters which are obtained from experimental field data or from continuous models assuming one-mode approximation for extensional, flexural and torsional vibrations. However, the lumped parameter models do not include dynamical effects due to geometrical non-linearities. In this context, the objective of present work is to analyze the effects of geometrical non-linearities due to initial stresses in the vibration of drill-strings together with the patterns of vibroimpact and comparing the results with the predictions of linear models. The beam model is discretized using a finite element with 12 degrees of freedom. The results have shown an important influence of the geometric non-linearities (when compared with the predictions of a linear model) in the dynamic responses of the drill-strings, especially when the beam undergoes impact patterns with the borehole or the rock formation. This influence can be observed in the calculation of reaction forces at top position as well as the time histories of radial displacements.