Using the ultrasonic technique with high precision, the sound velocities of tetragonal crystal YVO₄, 1at-% Nd:YVO₄and 2at-% Nd:YVO₄have been measured at the ambient temperature and pressure by the pulse echo overlap method. Six independent second order elastic constants (C₁₁,C₄₄,C₆₆,C₃₃,C₁₂and C₁₃) of crystals and Debye temperature ΘD have been obtained from longitudinal and shear velocities propagated along different orientations. The results indicate no change of these parameteres with different Nd3+ concentrations. An abnormal phenomena on C66 was observed with putting a pair of compressive force on (010) faces of the crystal along polarisation direction ［010］ of the transducer.