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In this paper, we developed a methodology for estimating three parameters of tissue inclusion: size, depth, and Young's modulus from the tactile data obtained at the tissue surface with the tactile sensation imaging system. The estimation method consists of the forward algorithm using finite element method, and inversion algorithm using artificial neural network. The forward algorithm is designed to comprehensively predict the tactile data based on the mechanical properties of the tissue inclusion. This forward information is used to develop an inversion algorithm that will be used to extract the size, depth, and Young's modulus of a tissue inclusion from the tactile image. The proposed method is then validated with custom made tissue phantoms with matching elasticities of typical human breast tissues. The experimental results showed that the proposed estimation method estimates the size, depth, and Young's modulus of tissue inclusions with root mean squared errors of 1.25 mm, 2.09 mm, and 28.65 kPa, respectively.