A finite element algorithm to simulate two dimensional flows of viscous and inviscid compressible fluids for a wide range of Mach numbers is presented in this work. This model is coupled to immersed deformable structures through equilibrium and compatibility conditions in order to analyze its dynamic behavior. For the fluid, time integration is performed by a two-step Taylor-Galerkin explicit scheme and Newmark’s method is used to obtain the dynamic response of the structure. An arbitrary mixed Euler-Lagrange description is used to re-define a new finite element mesh in the presence of the immersed structure displacements. Finally, several examples are included showing the model behavior and possibilities for future expansions.