In this chapter, dynamics of an idealized lattice is discussed as an approximate model for practical crystals in complex structure. Lattice vibrations in propagating modes represent fundamental excitations in the periodic structure, being characterized by frequencies and wave vectors distributed in virtually continuous spectra. Quantum theoretically, the lattice dynamics is represented by a phonon gas, where phonon quanta behave like classical particles. On the other hand, lattice excitations at low frequencies can be responsible for the strained structure. For thermoelastic properties of crystals, such excitations play essential roles, depending on thermal and mechanical conditions of the surroundings.