We describe a new method for computing an arbitrary number of eigen solutions of a given aeroelastic problem. The proposed method is based on the re-engineering of a three-way coupled formulation previously developed for the solution in the time domain of nonlinear transient aeroelastic problems. It is applicable in subsonic, transonic, and supersonic flow regimes, and independently from the frequency or damping level of the target aeroelastic modes. It is based on the computation of the complex eigen solution of a carefully linearized fluid/structure interaction problem, and relies on the inverse orthogonal iteration algorithm. We illustrate this method with the stability analysis of a flat panel with infinite aspect ratio in supersonic airstreams and the AGARD 445.6 aeroelastic wing. For these aeroelastic problems, we show that the results produced by the proposed eigen solution method are in excellent agreement with those predicted analytically and numerically as well as with experimental data.