Effects of fluid-structure coupling on the dynamic behaviour of flexible airship can be modelled with a potential, incompressible, inviscid flow. A new formalism to study linear variations of the flow induced on the fluid-structure interface in a time dependent ambient flow is introduced. The features of the Boundary Element Method used to solve this problem numerically are exhibited. Numerical results of the linear model are compared with analytical and non linear numerical results, assessing the validity and the limitations of the approach