SUMMARYThe paper develops a coupled approach to simulate an axisymmetric explosion inside a buried lined cavity. The approach allows accounting for all the stages of the process: detonation of the internal charge; the shock wave propagation in the internal gas with further interaction with the lining, including multiple reflections; soil-structure dynamic interaction, including multiple gap openings and closures and wave propagation in the surrounding compressible plastic medium.The interaction problem is solved by a combination of the variational difference method and of the modified Godunov's method based on the fixed Eulerian mesh with the so-called mixed cell. The contact pressures acting on the lining due to both detonation products and soil-lining interaction are computed through the solution of the joint system of finite difference equations of gas, shell and soil dynamics using a simple iteration method.