In addition to mathematical advances and very promising practical applications, the study of Nonlinear Acoustics now is leading to fundamental advances in Solid State Physics. Nonlinear distortion of an ultrasonic wave in a solid is controlled by a nonlinearity parameter which is a function of the third-order elastic (TOE) constants as well as the second-order elastic (SOE) (the usual) elastic constants. Measurement of the waveform distortion, then, makes possible the evaluation of the TOE constants, because the SOE constants can be evaluated from ultrasonic wave velocities. The number of elastic constants is determined by the crystal symmetry. The magnitude and sign of the TOE constants are determined by intermolecular forces. In a cubic crystal in which central forces and nearest-neighbour interactions exist one would find C111 = 2C112 = 2C166 and C 123 = C456 = Cl44 = 0 in the limit of 0°K. Over the past several years we have measured TOE constants as a function of temperature down to 3°K in such crystals as germanium and copper and in amorphous fused silica. A summary of presently available data is presented, and a comparison of the behaviour of the intermolecular forces for different types of crystals is made. Recently we have found that in copper central forces and nearest-neighbour interactions seem to predominate in determining TOE constants, but this does not happen near 0°K as expected. It seems to happen near 40°K and again at 190°K.