In this paper we prove the strong unique continuation property for an elasticity system with small residual stress. This system is not isotropie due to the existence of the residual stress. Therefore, it is impossible to reduce the principal part of the system to uncoupled Laplacian operators as we have for the isotropic elasticity system. Also, the coefficients of the system are allowed to have some singularities. The proof of the main theorem is based on Carleman estimates with singular weights.
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