It is difficult to answer how many elastic waves exist in anisotropic solids. The traditional viewpoint believes that there are only two bulk elastic waves in solids, one is the dilation wave discovered by Poisson in 1892, and the other the shear wave discovered by Stokes in 1899. The existence of the P-wave and the S-wave was also verified by the classical elastic theory. However, with the discovery of some new phenomena of elastic waves in anisotropic solids, it is found that the limitations of classical elastic theory have become obvious. Furthermore, the current concepts and theories of elastic waves can not answer several basic questions of elastic wave propagation in anisotropic solids. For example, how many elastic waves are there? How many wave types are there? What is the space pattern of elastic waves? As we know, the Christoffel’s equation, which is often used to describe anisotropic elastic waves in the classical elastic theory, can not indicate the space pattern and the complete picture of elastic wave propagation in anisotropic solids, but only show the difference of propagation in the different directions along an axis or a section (Vavrycuk, 2005). The reason for this is that the classical elastic wave equations, expressed by displacements can not distinguish the different elastic sub-waves (except for isotropic solids), because the elasticity and anisotropy of solids are synthesized in an elastic matrix. Similarly, for the electromagnetic fields, except for the Helmholtz’s equation of electromagnetic waves in isotropic media, the laws of propagation of electromagnetic waves in anisotropic media are also not clear to us . From the Maxwell’s equation, the explicit equations of electromagnetic waves in anisotropic media could not be obtained because the dielectric permittivity matrix and magnetic permeability matrix were all included in these equations, so that only local behaviour of electromagnetic waves, for example, in a certain