The third‐order elastic constants of germanium, magnesium oxide, and fused silica have been measured using the pulse superposition method for determining the ultrasonic velocity as a function of both uniaxial and hydrostatic pressure. From these measurements all six third‐order elastic constants were calculated by using the equations of Thurston and Brugger for MgO and Ge, and the three independent isotropic third‐order constants were calculated for fused SiO2.The results for Ge are in good agreement with the most recent data of McSkimin and Andreatch. The results for MgO agree in part quite well with theoretical data calculated from a Born‐Mayer potential. Drastic failure of the three Cauchy relations indicates the presence of many body forces. For fused silica, the remaining Cauchy relation is, as may be expected, not well fulfilled.