In this paper we consider an elasticity system with residual stress. The constitutive equation of this elasticity system differs from that of the isotropic elasticity system by R + (∇u)R, where R is the residual stress tensor. This system is not isotropic due to the existence of the residual stress R. Thus, it is not possible to reduce the principal part of the system to uncoupled wave operators as we have for the isotropic elasticity system. Here we investigate inverse problems of identifying the force term or the density by a single measurement of the lateral boundary. We establish uniqueness results by means of Carleman estimates when the residual stress is small.