Abstract: There exist kinds of micro-cracks at mesoscopic size non-uniformly distributed in elastomer materials during early stage of degradation,which could induce strongly Non-classical Nonlinear Acoustic Wave(NNAW) propagation.The propagation of NNAW in a conical bar embedded with micro-cracks is investigated based on Preisach-Mayergoyz(PM) space model,and the exact equations for quasi-analytic harmonic excited by micro-cracked region are derived.The theoretical calculation and the experimental results show that the strong odd harmonics due to NNAW are obviously observed,whose displacement amplitudes are closely related to the position and width of the micro-cracked region as well as the strength parameter of the non-classical nonlinearity.Based on these characteristics of NNAW,the amplitude coefficients of the third(or fifth) harmonics are employed to discern and locate the micro-cracked region.