The structure and elasticity of tricalcium aluminate (C3A) have been experimentally and theoretically studied. From high-pressure X-ray diffraction experiments, the bulk modulus of 102(6) and 110(3) GPa were obtained by fitting second- and third-order finite strain equation of state, respectively. First-principles calculations with a generalized gradient approximation gave an isotropic bulk modulus of 102.1 GPa and an isothermal bulk modulus of 106.0 GPa. The static calculations using the exchange-correlation functional show an excellent agreement with the experimental measurements. Based on the agreement, accurate elastic constants and other elastic moduli were computed. The slight difference of behavior at high pressure can be explained by the infiltration of pressure-transmitting silicone oil into structural holes in C3A. The computed elastic and mechanical properties will be useful in understanding structural and mechanical properties of cementitious materials, particularly with the increasing interest in the advanced applications at the nanoscale.