Starting from a Finite-Volume Method solving the Navier-Stokes equations for compressible fluid flow and a Finite-Element Method based on quasi one-dimensional Timoshenko beam elements for structural dynamics, a numerical method for coupled aeroelastic problems of flight vehicles is developed. Using the method, extended aerodynamic stability derivatives can be obtained by Computational Aeroelastic Simulation (CAS). Stability derivatives are derivatives of global aerodynamic quantities like lift and drag coefficients with respect to significant generalised coordinates and velocities characterising the flexible aerodynamic configuration of a deformable light-weight flight vehicle. The numerical method facilitates the study of excitation of structural vibration modes by coupling with unsteady flow processes. Determining experimentally the aeroelastic stability derivatives for complex configurations would be an extremely difficult task. In such cases, CAS may better support light weight construction optimised with respect to flight stability. On the flow side the coupled method is based on the DLR FLOWer code which solves the Reynolds-averaged Navier-Stokes equations employing central differencing on structured multi-block grids. Several numerical standard techniques for simulating supersonic, unsteady, turbulent flow are employed and have been partly extended in the code, e.g. unsteady inflow/outflow conditions. The quasi implicit time integration based on Jamesons Dual Time-Stepping (pseudo-time stepping) is synchronised with the Finite-Element Method for the structure which at the same time forms the basis of the multi-block grid deformation algorithm implemented in this work for the flow solver FLOWer. By exemplary computations it is shown that an explicit algorithmic coupling of the two methods has been realised which consistently captures unsteady fluid-structure processes. The developed new modules are tested against results taken from the literature. The coupled code has been validated by comparison with experimental results obtained in the Collaborative Research Center SFB 401 "Flow Modulation and Fluid-Structure Interaction at Airplane Wings" with an elastic rectangular wing of finite span. Based on this, computational aeroelastic simulations and numerical analyses of generic flight structures (bodies of revolution with fins) are performed which include direct aerostructural free flight simulation of a rigid and an elastic flying vehicle. It is shown how to use extended aeroelastic derivatives for control manoeuvres of flying elastic bodies. The selection of slender bodies of revolution was made to restrict the number of variables to be surveyed. From the results one may conclude that ignoring the degrees of freedom of elastic deformation may cause intolerable deviations from the real flight dynamical properties of the configuration. Operating numerically in a far-reaching optimisation parameter field concerning light weight construction and real-time flight dynamics, it seems not possible to be done without taking into account the complete set of nonlinear aeroelastic equations of motion and using CAS to a major extent.