Our objectives for this 10 week feasability study were to gain an initial theoretical understanding of the numerical issues involved in modeling fluid-structure interface problems and to develop a prototype software infrastructure based on deforming composite grids to test the new approach on simple problems. For our first test case we considered a two-dimensional fluid-solid piston problem in which one half of the domain is occupied by fluid and the other half by a solid. We determined the exact solution to this problem using the method of characteristics and d'Alembert's solution to the wave equation. We solved this problem using our new numerical approximations and veried the results compared to the exact solution. As a second test case we considered a two dimensional problem consisting of a shock in a fluid that strikes a cylindrically shaped solid.