The drill-strings used in drilling operate under extreme condi-tions, therefore, an accurate understanding of their dynamics is necessary and has attracted much interest. Although a bottom hole assembly (BHA) is to a great ex- tent responsible for the dynamics of the system, the in uence of the drill-pipes has been increasingly neglected by current models. Their dynamics and geometrical behaviour should be better analysed for a deeper understanding of underlying phe- nomena. For example, under stick-slip oscillations, the torque on the drill-string may cause torsional buckling of the drill-pipes, incurring in helical con guration, in which the apparent length is reduced, a ecting the forces at the bit{rock interface. With such behaviour and interactions in mind, this work focuses on elaborating a comprehensive mathematical model to investigate the dynamics of drill-strings, with attention to the drill-pipes section. Firstly, lower dimensional models are used to analyse the stick-slip limit cycle and its limits of existence. Then, a model developed for MEMS is used as a base for a comprehensive model using the formu- lation of Cosserat rods. Relevant boundary conditions are applied and a numerical simulation procedure is established. Simulations are performed for a range of sce- narios under stick-slip occurrence, and the behaviour of the drill-pipes is analysed. Focus is then given to axial vibrations with bit-bounce and the in uence on stick- slip, later to lateral vibrations with whirling motion of the drill-pipes, and nally to helical con gurations, taken by the drill-string under combined torsional, axial and lateral loads, showing the consequent shortening of the drill-string.