A newly developed theory on plasticity makes it possible to include elastic effects, which play a major role when using blunt hardness indenters. This article reviews the new theory and explains several phenomena associated with practical hardness testing. In the indentation hardness test, a blunt indenter that approximates a flat punch is forced into a plane surface. The effective cone angle for most indenters is such that some upward flow results even when there is sufficient material surrounding the indenter to provide a full elastic constraint. When loaded by a blunt indenter, materials with high values of Young's Modulus of Elasticity/uniaxial flow stress (E/Y) (metals) appear to develop a Hertzian stress distribution over the contact. In contrast, materials with low values of E/Y (glasses and polymers) develop a uniform distribution of stress.