The recent interests [1–5] on the Lamb wave study of orthotropic sheet materials have been motivated by nondestructive evaluation (NDE) and characterization of the fiber composite plate. The dispersive properties of Lamb waves in an isotropic plate have been well known since the original work of Lamb [6]. However, the problem of Lamb waves in anisotropic plates is, as yet, largely unexplored. For the propagation of elastic waves in composites reinforced with large diameter fibers, such as the SiC fibers employed to reinforce both ceramic and metallic matrix materials, the dynamic effects of the microstructuring must be considered if the fiber is large enough to equal a longitudinal acoustic quarter-wavelength in the range of 10 to 20 MHz. However, in most fiber composite systems, the fiber diameter is small enough to permit modelling of the material as a homogeneous, but anisotropic, medium which retains the symmetry of the composite, but ignores its microstructural nature.