A new approach for analyzing indentation plasticity and for determining indentation stress fields is presented. The analysis permits relations to be established between material properties (notably hardness, yield strength, and elastic modulus) and the dimensions of the indentation and plastic zone. The predictions are demonstrated to correlate with observations performed on a wide range of materials. The indentation stress fields are computed along trajectories pertinent to three dominant indentation crack systems: radial, median, and lateral cracks. The peak load and residual tensile stresses are shown to be consistent with observed trends in indentation fracture.