Abstract: basic equation of non-ordinary state-based peridynamic theory is deduced at first,then damage theory is introduced, Its numerical program is compiled after the basic equation of non-ordinary state-based peridynamic theory is discretized. The rupture and non-rupture problem of a tensile plate with circular hole is modeled using non-ordinary state-based peridynamic theory. The numerical results show that it can not only model rupture problem but also non-rupture problem by using non-ordinary state-based peridynamic theory. In comparison with the other numerical methods, the propagation and coalescence of cracks can be simulated using non-ordinary state-based peridynamic theory without any outer fracture criterion. Therefore, it has great advantages over other numerical methods. And it also offers a new method and thought to simulate the rupture problem of materials.