Abstract: A method of the non-collinear wave mixing was adopted to localize the plasticity at the crack tips.For the nonlinear mixing of the bulk waves,the resonance conditions were theoretically investigated based on the perturbation approach and vector analysis.It is numerically demonstrated that the longitudinal wave generated by the non-collinear mixing of the shear waves is sensitive to the plastic zone.In addition,experimental investigations were conducted for localizing the plasticity at the crack tips in the specimens of 7075-T6 aluminum alloy.Two pairs of shear waves with the frequencies of 5 MHz-5 MHz and 4.75 MHz-5.25 MHz,were selected as the primary waves,respectively.The acoustic nonlinear parameters were utilized to characterize the plasticity state at the crack tips.It is illustrated that the maximums of the acoustic nonlinear parameters occur at the areas ahead of the notch,which exactly are the plastic zones around the crack tips.Therefore,the non-collinear wave mixing may be a potential way to locate the plasticity at the crack tips.