High precision force-displacement measurements of various forms of glassy and graphitic carbon have been made with a Berkovich and spherical tipped indenter. The force-displacement data show almost complete recovery despite contact pressures exceeding a considerable fraction of the elastic modulus. With a spherical tipped indenter the transition from elastic to inelastic response could be readily identified. It was found that the extent of the hysteretic response with a spherical indenter increased with increasing load. Only minor differences in the force-displacement response of crystalline graphite indented normal to the basal plane and the glassy carbon was identified. A simple model for interpreting the force-displacement data is developed. These results are compared with indentations made on diamond like carbon films on various substrates.