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This paper studies the equilibrium structure parameters "and the dependences of the elastic properties on pressure for rutile TiO2 by using the Cambridge Serial Total Energy Package (CASTEP) program in the frame of density functionaltheory. The obtained equilibrium structure parameters, bulk modulus B0 and its pressure derivative B’0 are in good agreement with experiments and the theoretical results. The six independent elastic constants of rutile TiO2 under pressure are theoretically investigated for the first time. It is found that, as pressure increases, the elastic constants C11,C33, C66, C12 and C13 increase, the variation of elastic constant C44 is not obvious and the anisotropy will weaken.