Gas foil journal bearings (GFJBs) have been widely employed in high-speed rotating machinery in the aviation industry. However, the role of fluid–structure interaction in the unsteady aerodynamic character of the gas film and the dynamic response of the elastic foils have not yet been clarified. In this study, an unsteady shearing flow interacting with an exciting deformation of the top or bump foils was investigated by means of a large eddy simulation with bidirectional fluid–structure interaction (BFSI). The result shows that the main frequencies and amplitudes of stable fluctuations of different flow field parameters at different positions are different. The oscillating duration in the solid domain is much less than that in the fluid domain. The main positions for the interaction between the gas film pressure and the elastic foil are on both sides of θ = π. Compared with the case without FSI, the presence of the elastic foil flattens the distribution of the pressure of the gas film. As the rotational speed increases, the main frequency and the amplitude of pressure in the fluid domain continuously increase. With FSI, there is no interference frequency near the main frequency, which improves the stability of the shearing flow. However, an interference frequency appears near the main frequency of total displacement in the solid domain. The analysis in this paper lays the foundation for unsteady fluid–structure interaction research.