The changes on aircraft structures and the increased use of advanced and light materials have led to the design of more efficient and flexible aircraft. This implies that rigid body dynamics are no longer sufficient to describe the aircraft behaviour in atmospheric flight. Furthermore, the frequencies of the lower structural modes are close to the frequencies of the rigid aircraft dynamics and, thus, a possible coupling between structural dynamics and piloting task must be taken in consideration during aircraft modelling. In this thesis, an analytical method, based on a mixed Newtonian-Lagrangian approach, is used to derive a simplified model of the flexible aircraft which maintains a "strong" link with the rigid aircraft equations of motion.