We describe a method for fluid-structure interaction with the interface and free surfaces defined by level sets. The fluid is treated by an Eulerian mesh whereas the solid or structure by a Lagrangian mesh. The level set method provides a compact framework for writing the weak form and for developing and computing the discretized equations. Lagrange multiplier methods and penalty methods are used to couple the fluid and structure. Results are presented for a few compressible fluid problems representative of high pressure waves.