In this work, we consider a high-order ADER-DG scheme for a two-phase model for compressible fluid flows in elastic media. The presented model takes its foundation from the theory of symmetric hyperbolic and thermodynamically compatible (SHTC) systems forwarded by Godunov, Romenski and collaborators, and is obtained as a combination of the Romenski model for two-phase flows, studied in [1, 2, 4], together with the Godunov-Peshkov-Romenski unified model for viscoelastic media [3]. The resulting hyperbolic PDE system is solved using a high-order ADER discontinuous Galerkin method with a posteriori sub-cell finite volume limiter to deal with shock waves and steep gradients in the volume fraction. Several test cases will be presented in one and two spatial dimensions, as to provide evidence of the approach’s validity. REFERENCES [1] Romenski, E., Resnyansky, A., Toro, E.: Conservative hyperbolic formulation for compressible two-phase flow with different phase pressures and temperatures. Quart. Appl. Math. 65(2), 259–279, 2007. [2] Romenski, E., Drikakis, D., Toro, E.: Conservative models and numerical methods for compressible two-phase flow. J. Sci. Comput. 42, 68–95, 2010. [3] Romenski, E., Reshetova, G., Peshkov, I., Dumbser, M.: Modeling wavefields in saturated elastic porous media based on thermodynamically compatible system theory for two-phase solid-fluid mixtures, Computers & Fluids, 206, no. 104587, 2020, [4] Rio-Martin, L., Dumbser, M.: High-order ADER Discontinuous Galerkin schemes for a symmetric hyperbolic model of compressible barotropic two-fluid flows, Commun. Appl. Math. Comput, 2023.