In this study, a new fluid structure interaction (FSI) algorithm is developed for the aerodynamic-elasticity problem, aiming to address the coupling problem between compressible fluids and deformable solid structures. To verify the feasibility of the proposed model, a two-dimensional cantilever panel case under shock waves was conducted. Our numerical results present good consistency with the data from literatures. Furthermore, the validated FSI algorithm is applied on an elastic spike under compressible hypersonic flow. The complicated interaction between the fluid and solid structure under various spike geometry sizes and materials were revealed in respect of the spike deformation, pressure, temperature, and flow fields distribution. The main findings show that the spike deformation largely affects pressure and temperature on the blunt, the aerodynamic drag and lift force, indicating the necessity of FSI. For the spike diameters and lengths, it is found that larger spike diameters and shorter spikes benefits for deformation reduction, thereby minimizing fluctuations in aerodynamic drag force. For spike materials, spikes with larger elastic moduli and lower densities are preferred for the drag reduction. Thus, the proposed FSI model can accurately predict flow fields around and deformations for elastic spikes and offer guidance for drag reduction design in aerospace engineering.