Based on the fundamental piezoelectric Christoffel's equation, we derived the expression of the elastic constants for piezoelectric crystal with trigonal symmetry point group 3 m. The ultrasonic wave velocities in LiNbO3 crystal, propagating along different crystallographic directions, are determined by the "pulse echo overlap method". The. carrier frequency of rf pulse is 10 MHz. The Values of the secondorder elastic constants CijE and CijD for LiNbO3 crystal are obtained as follow: C11E = 19.89, C12E = 5.25, C13E = 7.81, C14E = 0.96, C33E = 25.44, C44E = 6.10, C66E=7.32×1010N/m2·C11D = 21.51, C12D= 3.65, C13D = 7.91, C14D=-1.41, C33D = 26.10,C44D = 9.62, C66D = 8.93×1010N/m2.