Functionally Graded Materials (FGM’s) are inhomogeneous composites which are characterized with the gradual variation of their constituents. Because of this specific property, FGM plates show high resistance against mechanical loadings in addition to considerable durability in thermal environments. Hence, FGM plates have found extensive applications in various industries, especially aerospace ones. Furthermore, ultrasonic elastic waves play a major role in performing non-destructive evaluation. Therefore, it is necessary to know the behaviour of these waves particularly in heterogeneous media. Approximate plate theories might be considered as simple alternatives for sophisticated elastodynamics solution to carry out wave propagation analysis in plates. To employ plate theories for this purpose, detecting a compromise between simplicity and accuracy of numerical results is a serious concern. This problem is the main topic of the present thesis. In this research, investigation is done for infinite FGM plates in different cases of high frequency dynamic loadings and for various plate thicknesses as well as several heterogeneity amounts. Based on the obtained results, the reliability range of the plate theories for flexural wave propagation analysis in inhomogeneous FGM plates are illustrated. A hybrid numerical method (HNM) is employed to validate the results of plate theories. This method that uses layer elements is a combination of modal analysis and Fourier transform. Moreover, some other issues such as effects of in-plane forces and elastic foundations on the wave motion in FGM plates are studied. Also, the inverse procedure for recovery of impact load is discussed. Keywords Wave Propagation, FGM Plate, Plate Theories, Hybrid Numerical Method