Mechanical properties of materials in small-scale applications, such as thin coatings, are often different from those of bulk materials due to the difference in the manufacturing process. Indentation has been a convenient tool to study the mechanical properties in such applications. In this paper, a numerical technique is proposed that can identify the mechanical properties using optimization and evaluate the robustness of identified material properties using sensitivity analysis. First, two response surfaces are constructed for loading and unloading curves from the indentation experiment of a gold film on the silicon substrate. Unessential coefficients of the response surface are then removed based on the test statistics. Unlike the traditional methods of identification, the tip geometry of the indenter is included because its uncertainty significantly affects the results. In order to validate the accuracy and stability of the method, the sensitivity of the identified material properties with respect to each coefficient is analyzed. It turns out that the plastic hardening parameter is the most sensitive to the experimental data. In addition, all material parameters are sensitive to the coefficients of higher-order bases. However, their effects are diminished because the magnitudes of these coefficients are small.