The harmonic generation due to the third-order elastic (TOE) constants in germanium and gallium arsenide, and the nonlinear current-jump effect due to the fourth-order elastic constants in a quartz plate have been investigated. The complete TOE constants were determined from the measurement using an optical interferometer and from the values derived from the valence-force field theory. They showed a good agreement with those obtained by other experimental techniques. A phenomenon analogous to the hybride optical bistability was observed in a thickness-shear mode quartz resonator, and this was analyzed in terms of an equivalent nonlinear network.