An earlier optimisation approach proposed by Luo et al. [Luo, J., Lin, J., Dean, T. A., 2006. A Study on the Determination of Mechanical Properties of a power-law Material by Its Indentation Force-Depth Curve. Philosophical Magazine, 86(19), 2881-2905], which is based on the assumption that the instrumented indentation force-depth response of an elastic-plastic material is a linear combination of the corresponding elastic and elastic-perfect plastic materials, is extended in this work to extract mechanical properties of a power-law material from two given experimental indentation P-h curves for conical indenters of half included angles of 60°and 70.3°. It was found that the non-uniqueness problem encountered in the single P-h curve optimisation approach is effectively removed by the two P-h curves optimisation. The appropriateness of the use of second half included angle of 60°is discussed. For the five representative materials Al, Ti, Fe, Ni and steel, it was found that the maximum relative prediction errors for E, r y and n are 2%, 10.4% and 11.3%, respectively. The prediction accuracy of mechanical properties E, r y and n is generally better than other methods reported in the literature.