Rigid and fluid interaction problems are solved by the level set method with the RKDG method. The system of the Eluer equations are solved by the RKDG method while the level set equation which describes the motion of the interface are solved by high-resolution WENO finite difference scheme. The extended ghost fluid method is used to deal with the solid and fluid boundary. Numerical tests on two dimensional flow are carried ou and satisfactory results are obtained. This method can be extended to three dimensional questions since no mesh modification is needed.