Using Langevin dynamics simulations, we study effects of the shear force on the rupture of a double stranded DNA molecule. The model studied here contains two single diblock copolymers interacting with each other. The elastic constants of individual segments of diblock copolymer are considered to be different. We showed that the magnitude of the rupture force depends on whether the force is applied at 3' - 3' - ends or 5' - 5' - ends. Distributions of extension in hydrogen bonds and covalent bonds along the chain show the striking differences. Motivated by recent experiments, we have also calculated the variation of rupture force for different chain lengths. Results obtained from simulations have been validated with the analytical calculation based on the ladder model of DNA.