We report the Young's modulus of a series single-wall carbon nanotubes(armchair type and zigzag type)and BN zigzag type nanotubes on the basis of ab initio theory. According to the calculations, the relation between Young's modulus and the diameter of nanotubes is presented. We have also discussed how the strain energy of rolling effect of all kinds of nanotubes and how the balance basis set a of nanotubes varies with the type of nanotubes.