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The nearly cloaking via transformation optics approach for the isotropicelastic wave fields is considered. This work extends the study of the nearlycloaking scheme to the elasticity system with residual stress in \mathbb{R}^{N}for N=2,3, which is an anisotropic elasticity system. It is worth to mentionthat there are no minor symmetric properties for the elastic tensor withresidual stress and this system is invariant under a coordinate transformation.Therefore, we think the elasticity system residual stress model is more naturalthan the isotropic elasticity system in designing the elastic cloaking mediumin the physical sense. In addition, the main difficulty of treating thisproblem lies in the fact that there are no layer potential theory for theresidual stress system. Instead, we will derive suitable elliptic estimates forthe elasticity system residual stress by comparing with the Lam\'e system toachieve desired results.

Nearly cloaking for the elasticity system with residual stress