In the beginning of the chapter basic principles for constructing mathematical models of wave motion are given. Thereupon, a hierarchical model of microstructure, based on Mindlin’s ideas is deduced. In the one-dimensional case a corresponding system of 2 equations of motion is obtained. This system is later on referred to as the coupled system. Further, making use of the slaving principle, the coupled system is reduced to a single approximate hierarchical equation of motion. For further purposes, linear and nonlinear cases are distinguished. The coefficients of the coupled system and the hierarchical equation are related to the density, free energy parameters and other physical features of the microstrucured material. The chapter ends with a general formulation of inverse problems to determine these coefficients.