In this paper a continuous model is presented that by finite element discretization is employed in the analysis of coupled extensional flexural and torsional vibrations of a drill-string. The drill-string is described as an axially rotating beam constrained to move inside a rigid cylinder that simulates the walls of the perforation hole. The beam is subjected to its own weight, reaction forces and perturbation bending moments acting in the drill-bit. The friction and the lateral impacts of the drill-string are considered by means of simplified schemes. Due to its inherent complexity, the dynamics of a drill-string is normally analyzed by means of models with lumped parameters, whose features are obtained by correlation with experimental data collected in the oil felds. However these lumped-parameter models do not include in a realistic way effects, such as geometric stiffening among others, that are quite important in flexible structures. There are some continuous models of drill-strings based on linear approaches and also accounting for geometric stiffening. Under this context, the objective of the present work is devoted to analyze, and compare with other approaches, the influence of geometric non-linearity together with patterns of vibro-impact in the dynamics of drill-strings. The continuous drill-string model is discretized by means of a beam-type finite element with 12 degrees of freedom per element. The results of this study show the in°uence of the considered effects in the dynamic response of drill-strings, especially when they are subjected to strong vibro-impact patterns with the walls and the bottom rock formation.