In this study, the acoustic emission characteristics of a rectangular plate with a partially covered free damping viscoelastic layer excited by an acoustic source (Hsu-Nielsen) has been investigated. A partially covered plate configuration consisting of a base plate (aluminum) and free damping layer (polyethylene) is considered. An acoustic emission source generated different acoustic modes, which caused the plate to have in-plane and out-plane displacements. These plate displacements will be captured by acoustic sensors. To obtain the general form of plate displacements theoretically, Von Karman theory and a Kelvin-Voigt model were used and the equations of motion were derived using Galerkin’s method. The effects of nonlinear terms of the strain-displacement relation on wave propagation characteristics of plates were investigated. The main frequency ranges of signals and the propagation speed of acoustic modes and their attenuation are very important for source locating. These parameters depend on the acoustic source and transmitted medium. So, theoretically predicting the main frequency range of signals because of the acoustic source and propagation characteristics of different acoustic modes has an important role in an acoustic source–locating algorithm. For this purpose, acoustic emission experiments were carried out using two R15α sensors. Frequency domains of theoretical and experimental results were analyzed. A comparison of the obtained results showed good agreement between the experimental and theoretical Lamb velocities and main frequency ranges.