A computational model of interaction of a compressible fluid and deformable elastic solid is presented. The model is derived from the general solid-fluid two-phase mixture model and its derivation is based on the Symmetric Hyperbolic Thermodynamically Compatible (SHTC) systems theory. The governing equations form a symmetric hyperbolic system of partial differential equations of the first order, the solutions of which satisfy the thermodynamic law of conservation of energy. These properties allow the direct application of advanced high accuracy computational methods to solve model equations and ensure the reliability of numerically obtained solutions. Some preliminary results of numerical simulation are presented, showing the applicability of the model for studying complex problems of the solid-fluid interaction.