Abstract: Non-destructive Testing(NDT) for solid is a top subject.Nonclassical nonlinear acoustic phenomena are shown in solid with cracks.In this paper,the propagation of sound wave and the nonclassical nonlinear acoustic properties in solid were studied theoretically and experimentally.The nonclassical nonlinear phenomena were observed experimentally in one dimension,the quadric relationships between the amplitude of odd harmonics and that of fundamental frequency were found,which were in agreement with the theoretical prediction.The sound transmissions through solid with dissipation and crack were simulated in two dimensions,the influence of classical nonlinearity and nonclassical nonlinearity on the sound propagation was discussed.And the crack was mainly contributed to the nonclassical nonlinearity.The relationship between the nonlinear parameter and the position and width of the crack was analyzed. The nonlinearity parameter was sensitive when the crack was at the symmetrical position near the center of the bar or near the source.However,there was no sensitivity to crack at the center of the bar or far away from the source.With the increase of width of the crack,the nonlinearity parameter also increased,however,it decreased before the crack was extended to the edge of the bar.