The dynamical behavior of the constituent atoms in the solid phase plays a significant role in the study of interaction of radiation and provides favorable means for adequate description of a large number of solid state phenomenon such as phonon dispersion curve, elastic and thermal properties, neutron scattering spin-lattice relaxation etc. During the past four decades of the lattice dynamics, the success of a lattice dynamical model is determined by its ability to explain the complete lattice dynamical properties. This book is an outcome of the efforts devoted to carry out a detailed and systematic theoretical investigation of the phonon dispersion, Debye temperatures variation, Two-phonon density of states and anharmonic elastic properties of gallium pnictides (GaP, GaAs and GaSb). The nature and the physical properties of the gallium pnictides have given an appealing interest in the study of their lattice dynamics. This has motivated the author to realize basic need of a lattice dynamical model for complete and satisfactory description of interesting phonon dispersion and associated physical properties derivable from the phonon spectra of the gallium pnictides.