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Finite element simulations were conducted to examine spherical indentation in the elastic – plastic transition regime. Various elastic-perfectly plastic materials were studied by varying the ratio of the elastic modulus to the yield stress in the range 25 – 1000. Special attention was given to the influence of residual stress and friction on the indentation load – displacement behavior and development of the plastic zone. A new method for measuring yield strengths from indentation load – displacement curves is proposed, and a recently developed experimental method for measuring biaxial residual stresses by nanoindentation methods is assessed. In the appropriate limits, the simulations show good agreement with the theoretical descriptions of spherical indentation given by Hertz and Tabor.