In this chapter, the governing equations for free vibration of isotropic plates of uniform thickness are presented, and the exact vibration solutions for plates of various geometries and boundary conditions are given. For a detailed derivation of the governing equations of plate motion, the reader may consult standard textbooks on plates such as Timoshenko and Woinowsky-Krieger (1959), Szilard (1974), Ugural (1981), Liew et al. (1998), Soedel (2004), and Reddy (2007).