This paper addresses a diagnostic palpation system based on the measurement of nonlinear elasticity. An indentation probe is used to press against breast tissue. Then, the measured reaction force is used to estimate the parameters of nonlinear elasticity, which enables the identification of tissue type, such as fat, muscle, mammary gland or tumor. Here, we present the basic concept of our study and preliminary experimental and simulation results from pilot studies. More specifically, we measured the nonlinear response of reaction force using the breast of a goat. In addition, we also simulated the reaction force using nonlinear biomechanical simulation with several tissue types. Large differences in reaction force occur only in the nonlinear range in both experimental and simulation situations. Our results confirmed the feasibility of our concept.