The modified ghost fluid method (MGFM) provides a robust and efficient interface treatment for various multi-medium flow simulations and some particular fluid-structure interaction (FSI) simulations. However, this methodology for one specific class of FSI problems, where the structure is plate, remains to be developed. This work is devoted to extending the MGFM to treat compressible fluid coupled with a thin elastic plate. In order to take into account the influence of simultaneous interaction at the interface, a fluid-plate coupling system is constructed at each time step and solved approximately to predict the interfacial states. Then, ghost fluid states and plate load can be defined by utilizing the obtained interfacial states. A type of acceleration strategy in the coupling process is presented to pursue higher efficiency. Several one-dimensional examples are used to highlight the utility of this method over loosely-coupled method and validate the acceleration techniques. Especially, this method is applied to compute the underwater explosions (UNDEX) near thin elastic plates. Evolution of strong shock impacting on the thin elastic plate and dynamic response of the plate are investigated. Numerical results disclose that this methodology for treatment of the fluid-plate coupling indeed works conveniently and accurately for different structural flexibilities and is capable of efficiently simulating the processes of UNDEX with the employment of the acceleration strategy.