A series of detailed measurements of the lattice absorption bands of gallium arsenide has been made over the wavelength range 10–40 &mgr; and over the temperature range 20–292°K. These results can be interpreted in terms of multiple phonon interactions involving five characteristic phonon energies. These results, along with the known elastic constants, have enabled us to supply all the relevant data for a computation of the complete phonon spectrum using an extension of the shell model.