Abstract: Because the equations of state are different, many difficulties will occur when we treat multimedium flow with general difference methods. Such problem has been successfully solved with the singularity-separating method. The main idea of the method is that we take all discontinuity lines, including the boundary lines between two mediums, as internal boundaries. A mixed scheme is used in each subregion. The values on the boundaries can be precisely determined. Not only can the difficulties caused by multimedium be overcome, but also the precision of the solution is high.