In this study a novel optimization approach is proposed to extract mechanical properties of a power law material whose stress - strain relationship may be expressed as a power law from its given experimental indentation P - h curve. A set of equations have been established to relate the P - h curve to mechanical properties E, sigma(y) and n of the material. For the loading part of a P - h curve this approach is based on the assumption that the indentation response of an elastic - plastic material is a linear combination of the corresponding elastic and elastic - perfect plastic materials. For the unloading part of the P - h curve it is based on the assumption that the unloading response of the elastic - plastic material is a linear combination of the full contact straight line and the purely elastic curve. Using the proposed optimization approach it was found that the mechanical properties of an elastic - plastic material usually cannot be decided uniquely by using only a single indentation P - h curve of the material. This is because in general a few matched sets of mechanical properties were found to produce a given P - h curve. It is however possible to identify the best matched set of mechanical properties by knowing some background information of the material. If the best matched material is identified, the predictions of mechanical properties are quite accurate.