This paper presents an efficient modelling of autonomous flexible airships. These flying objects lighter than air (L.T.A.) are assumed to undergo large rigid-body motion and small elastic deformation. The formalism used is based on the Euler-Lagrange approach. The airship considered in this study is represented by a flexible ellipsoid of revolution. The coupling between the added masses issued from the overall body motion and those issued from the elasticity was determined by means of the velocity potential flow theory. We develop a fully analytical methodology with some assumptions. This feature distinguishes the current work from earlier treatments of the coupling, it allows one to minimise the number of degrees of freedom of the dynamical model, and renders the model suitable for use in the algorithms of stabilisation and trajectory generation. Numerical simulations are presented at the end of this paper. They underline the interest of the developed theoretical results.