The investigation of flight dynamics instability, when based on computational fluid dynamics level aerodynamics, is traditionally done in the time domain. It is, however, possible to look to the behavior of the eigenspectrum of the Jacobian of the semidiscrete system to obtain information at a reduced computational cost. The central computational task in this approach is to solve a sparse linear system, with a key issue being the calculation of an effectiveparallelpreconditioner.Withaknowledgeofthebifurcationangleandthecriticaleigenvalue/eigenvector,it is possible to develop a reduced-order model which can predict the limit cycle amplitude postbifurcation. In this paper the shifted inverse power method, built on a preconditioned sparse matrix solver, is used to predict the wingrock onset angle of an 80-deg delta wing. The postbifurcation limit cycle oscillations are then calculated using a reduced model which uses knowledge of the critical mode of the system. This problem is considered here as a prototype flight dynamics instability.