我们采用超声“脉冲回波重合法”技术［１］，测定了立方晶体钇铝柘榴石（ＹＡＧ：）的二阶弹性常数，以及它们在静水压和单轴应力条件下，随压力变化，获得了三阶弹性常数．它们分别是：Ｃ１１＝３３４．７８ＧＰａ，Ｃ１２＝１０９．９５ＧＰａ，Ｃ４４＝１１５．２５ＧＰａ，和Ｃ１１１＝－３３７７．６６ＧＰａ，Ｃ１１２＝－８４１．１６Ｇｐａ，Ｃ１２３＝－３２．８６Ｇｐａ，Ｃ１４４＝－３７．６６Ｇｐａ，Ｃ１６６＝－５７９．３８Ｇｐａ，Ｃ４５６＝－１１４．６０Ｇｐａ．根据这些数据，我们还计算了ＹＡＧ：Ｎ＿ｄ￣（３＋）晶体的德拜温度以及Ｇｒｕｎｅｉｓｅｎ参数，以及ＹＡＧ：Ｎ＿ｄ￣（３＋）的状态方程． We measured the second-order elastic constants of cubic yttrium aluminum garnet (YAG :) by ultrasonic “pulse echo coincidence” technique [1], and measured their hydrostatic pressure and uniaxial stress with pressure changes, The third-order elastic constants are obtained. They are: C11 = 334.78 GPa, C12 = 109.95 GPa, C44 = 115.25 GPa, and C111 = -3377.66 GPa, C112 = -841.16 Gpa, C123 = -32.86 Gpa, C144 = -37.66 Gpa , C166 = -579.38Gpa, C456 = -114.60Gpa. Based on these data, we also calculate Debye temperature and Gruneisen parameters of YAG: N_d¯ (3+) crystal as well as the state equation of YAG: N_d¯ (3+).