An indentation method to determine equi-biaxial residual stress is proposed by examining the data from the incremental plasticity theory based FE analyses. We found that hardness is strongly dependent of the magnitude and sign of residual stress and material properties. We then selected some normalized parameters minimally affected by material properties and tip radius. With numerical regressions of the data obtained, we proposed new formulae for residual stress evaluation. The new approach provides a substantial enhancement in accuracy compared with the prior methods.