Abstract: Numerical simulation of multi-material compressible flow problem is of great importance in both the national defense and industry areas, such as weapon design and blast wave defense. Due to the property of large deformation and high nonlinearity, the efficient simulation of multi-material compressible flow becomes a quite challenging problem. A numerical scheme is developed to carry out the simulation of an immiscible multi-material compressible flow with sharp phase interface on two dimensional and three dimensional unstructured Eulerian grids, which can handle the large deformation of compressible fluid and elastoplastic solid under the extreme conditions. We use the level set method to depict the phase interface numerically, and explicitly reconstruct the phase interface in a piecewise linear manifold. The topological structure of the phase interface is constructed explicitly, which can handle any number of media in the whole computational domain and three media in a single cell. The traditional finite volume method is used to calculate the edge numeircal flux between the same material in adjacent cells, while the phase interface flux is calculated by exactly solving a one dimensional multi-material Riemann problem on the normal direction of the phase interface. The above procedures can keep the conservation of the phase interface flux, and the interaction between two media across the phase interface can keep consistent with the real situation. A robust aggregation algorithm is adopted to build cell patches and adjust the conservation variables around the phase interface, which can effectively remove the numerical instability due to the breakdown of the CFL constraint by the cell fragments. Some classical examples and application problems, such as one-dimensional multi-material Riemann problem, gas-bubble interaction problem, intensive airblast problem, sub-surface blast problem, and blast wave propagation in three dimensional sap, which have a good agreement with the corresponding analytical and experimental results, are presented to validate our numerical scheme.