Certain ceramic materials display an indentation response similar to that observed for ductile metals when loaded with a spherical indenter. This unusual behaviour, for what are nominally brittle materials, influences the mode of contact damage in applications such as machining, wear, impact damage and hardness testing. The shape of the plastic zone beneath the indenter is typically fully contained within the circle of contact on the specimen surface and thus conventional hardness theories, such as the popular expanding cavity model, provide an inadequate account of indentation response of the material. The present work demonstrates, by experiment, finite element modelling and theoretical considerations, that the indentation response is determined by the interaction between the evolving plastic zone and the mechanical properties of the specimen material, in particular, the ratio of the elastic modulus to the yield stress.