Abstract: Lamb wave propagation through fiber-reinforced composites has become a subject of intensive study due to its application to nondestructive evaluation. The anisotropic multilayered media are now usually studied by the transfer matrix formalism. Though this formalism is very convenient, it leads to numerical instabilities at high frequency-thickness products. The method developed in this paper using the global matrix is an improved version of Nayfeh's matrix method. The program using the global matrix has preferable stability, which can effectively create dispersion curves for Lamb wave propagation in anisotropic multilayered composites. Characteristics of Lamb wave propagation in fiber-reinforced composites are influenced by many factors and one of them is the number of layers. The calculated dispersion curves for different layered structures are presented together with plots of the through-thickness particle stress component amplitudes for two fundamental modes a₀ and s₀. These numerical examples provide a powerful tool for nondestructive evaluation of anisotropic layered plates.