Two interface capturing methods are studied for multi fluid flows, governed by the stiffened gas equation of state. The mixture type interface capturing algorithm uses a simple volume fraction model Euler equations written in a quasi conservative form, which is solved by a standard high resolution piecewise parabolic method (PPM) with multi fluid Riemann solver. The level set interface capturing method uses a narrow band ghost fluid method (GFM) with no numerical smearing. Several examples are presented and compared for one and two dimensions, which show the feasibility of the two methods applied to various multi fluid problems. Two interface capturing methods are studied for multi fluid flows, governed by the stiffened gas equation of state. The mixture type interface capturing algorithm uses a simple volume fraction model Euler equations written in a quasi conservative form, which is solved by a standard high resolution piecewise parabolic method (PPM) with multi fluid Riemann solver. The level set interface capturing method uses a narrow band ghost fluid method (GFM) with no numerical smearing. Several examples are presented and compared for one and two dimensions, which show the feasibility of the two methods applied to various multi fluid problems.