Abstract: It is important to deal with the material interfacesappropriately in multimaterial flows. ALE based on moving grids is applied tosolve 1-D multi-material Riemann problems and three methods of dealing withthe numerical flux on the material interface are proposed in this article:Lagrange method, GFM and HLLC method. According to the results obtained withthese methods, the performance of GFM and HLLC method is better and they give more accurate results thanLagrange method at the material interface with high grades of pressure.