In this paper we present a new robotic palpation method to perform quantitative measurement of the material parameters of human tissues, for use in medical applications. The proposed method is achieved by the use of a system that integrates a robotic component and a numerical simulation component. The robotic component is used to measure the contact force and displacement at each point on the human body contacted by a robotic probe. The numerical simulation component identifies the material parameters using the proposed method, where two data sources are used, namely, (1) the measured data from the robotic part, and (2) simulated deformation data obtained by the finite element method. In order to validate the proposed system, we report initial results from several phantom tissue experiments, which demonstrate the ability of the system to quantitatively determine the elastic moduli of tissues. We also discuss several potential challenges in the future of the proposed system.