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An iterative solution to the inverse problem of elasticity and viscosity is proposed in this paper. A finite elements model has been derived to account for the viscoelastic changes in soft tissue that is consistent with known rheological models. Using this deformation model and the observed dynamic data, the viscosity and elasticity have been reconstructed in the medium by using a Gauss-Newton based approach. Previous knowledge of the parameters on the boundaries of the medium are necessary to assure uniqueness and convergence and to obtain an accurate map of the viscoelastic properties. The methods have been studied in FEM simulations and also tested through experiments, where the viscosity and elasticity of a gelatin based phantom with an inclusion of known properties have been reconstructed successfully.