A theory formulated in 1916 by Horace Lamb predicting that plates may vibrate in up to an infinite number of modes is confirmed by a method described. The theory is extended to correlate experimental observations. Equations are developed relating phase velocity to frequency and plate thickness in terms of longitudinal and shear wave velocity. Families of curves are obtained for aluminum and zirconium. The distinguishing characteristics of the various modes are discussed in the light of potential nondestructive testing applications. It is shown that the interior particles are displaced in elliptical orbits, with vertical motions existing at the surfaces when the wave velocity is (2)½shear wave velocity, and horizontal surface motions existing for wave velocities equal to longitudinal wave velocity.