Hartree-Fock and hybrid DFT and Hartree-Fock methods am used to calculate Young modulus of carbon nanotubos on the basis of ab-initio theory with program Crystal03.Calculated result with Hartree-Fock approximation agrees with other theoretical and experimental ones-Result with hybrid DFT and Hartree-Fock is smaller.Young's modulus of C nanotube depends on geometric structure and electronic structure as well.