Doublet mechanics (DM) is applied to materials with dispersing property. The wave equation in multi-layered skin tissue is obtained through the method of DM in this article. By changing the Poisson ratio in melanoma skin tissue, the growth and spread of melanoma (Breslow thickness), the internode distance, the reflection coefficients of the longitudinal waves incident vertically in the multi-layered skin model are calculated. And the acoustic velocity and acoustic attenuation coefficient changing with tissue parameters are also calculated. The results show that we can synthesize the change of the number of the minimal reflection coefficient, acoustic velocity and attenuation coefficient to discriminate cancerous skin from normal skin within a certain frequency.