From the viewpoint of the three-dimensional theory of elasticity or piezoelectricity, the pure thickness modes of a plate treated in the previous chapter are waves with wave vectors along the thickness direction of the plate. The waves are bounced back and forth between the two major faces of the plate. These pure thickness waves can exist only in infinite plates. They are the idealized operating modes of many resonant piezoelectric devices. In reality, due to the finite size of a plate-like device, pure thickness modes are not possible. The operating modes of these devices are in fact related to three-dimensional waves whose wave vectors are slightly off the thickness direction of the plate, with a small component within the plane of the plate. From the view point of plate theories, these waves are long plate waves with in-plane variations that are slow as compared to the plate thickness. They will be called slowly varying thickness modes in this book. In this chapter we analyze slowly varying thickness modes in plates. Due to the in-plane variation of the modes, the problem becomes more complicated. Approximations are often needed in theoretical analyses. The in-plane variation of the modes results in many interesting and useful phenomena.