This chapter investigates the small deflection vibration of thin elastic plates bounded by the planes z = ±h/2, where h is the thickness of the plate. The equations of motion for a plate are developed and the procedure for solving the plate equations is illustrated for a plate simply supported on all edges. The resulting frequencies and mode shapes are presented for selected values of m and n. Solutions for alternate boundary conditions are also presented along with discussions of free and forced plate vibrations. In addition, the vibration of a specially orthotropic composite plate is discussed for free and forced vibrations. The equations of motion for a circular plate are developed based on cylindrical coordinates as opposed to Cartesian coordinates. Modes of free vibration for selected boundary conditions are presented based upon the use of Bessel functions. Forced vibrations are also discussed. Approximations to the solution of plate vibration problems using energy methods are presented focusing on the Rayleigh, Ritz, and Galerkin methods. The equations of motion for a sandwich plate are developed using the Reissner–Mindlin theory. Both free and forced vibrations of sandwich plates are discussed. The chapter culminates with discussions of the equations for plates with variable thicknesses.