This chapter introduces the basic finite element concepts and presents formulations for various applications, in particular for solid and structural analyses. The finite element method can solve differential equations whether they are boundary value problems, initial value problems, or eigenvalue problems. The chapter presents a shell formulation that can be easily degenerated into a plate or a beam element. For the shell formulation, we consider in-plane strains, transverse shear strains, and the transverse normal strain independently. The chapter shows that the natural frequency and the mode shape of the wet structure did not change as the fluid density was varied while the ratio of the speeds of sound of the solid and fluid media remained constant. Thus, the ratio of the speeds of sound is the main parameter that can affect the frequency as well as the mode shape.