The propagation of waves along an elastic layer has long been an area of active research since the later part of the 19th century. Many contributions have already been made to the study of wave propagation in a linear isotropic elastic layer and multi-layered (composites) structures, with traction-free boundary conditions on the upper and lower surfaces. However, for other types of boundary conditions the problem is significantly more involved, especially when multi-layer structures are considered. The aim of this thesis is to perform a complete asymptotic analysis of the dispersion relations for a symmetric three-layer laminate subject to free, fixed, and fixed-free face boundary conditions. The second goal is to construct appropriate asymptotic models for these boundary conditions. Chapters 2 and 3 are devoted to the study of a single-layer laminate subject to all three types of boundary conditions, while chapters 4-10 discuss the case of a three-layer structure. Chapter 4 is concerned with the derivation of the dispersion relation for an unstressed 3-layer laminate with free faces. The symmetry of the laminate allows one to consider separately symmetric and antisymmetric motion. The associated asymptotic models for long wave low and high frequency, symmetric and anti-symmetric motions are presented in Chapters 5 and 6. Chapter 7 contains the derivation and discussion of the dispersion relation for a threelayer laminate with fixed faces, resulting in appropriate asymptotic models for long wave motion in Chapter 8. Finally, in Chapters 9 and 10, the dispersion relation for 3- layer plate with one free and one fixed faces is derived and analysed using appropriated asymptotic models for low and high frequency motion.