Elastic properties of CaMnO3 are of primary importance in the science and technology of CaMnO3-based perovskites. From X-ray diffraction experiments performed at pressures up to 100 kbar using a diamond-anvil cell to hydrostatically compress our sample, a bulk modulus, K (0), of 1734(96) kbar was obtained after fitting parameters to the third-order Birch-Murnaghan equation of state. Mean field, semiclassical simulations predict, for the first time, the third-order equation-of-state parameters and show how the bulk modulus increases with pressure (the zero pressure value being 2062.1 kbar) and decreases with the extent of nonstoichiometry caused by the formation of oxygen vacancies. These trends are amplified for the shear modulus. A more accurate model that allows for the explicit reduction of Mn ions, or localization of excess electrons, yields qualitatively similar results. The experimental and calculated axial ratios show the same trends in their variation with rising pressure.