This chapter considers fluid—structure interaction problems, where the vibrations of the structure are the main interest, but its motion is affected by the flow of the surrounding medium, such as air or water. We review some basic concepts of fluid mechanics, and then systematically derive a Green’s function based analytical solution of the flow component of a simple fluid—structure interaction problem in two space dimensions. As the structure component in the fluid—structure interaction problem we consider traveling ideal strings and panels. In the numerical results, we examine bifurcations in the natural frequencies of the coupled system, for strings, and for linear elastic and Kelvin-Voigt viscoelastic panels. Whereas the natural frequencies of the traveling ideal string have no bifurcation points, bifurcations appear in the model with fluid—structure interaction whenever there is an axial free-stream flow.