A fundamental equation of state-based peridynamic theory is derived firstly from equating the traditional strain energy density to peridynamic ones and using the peridynamic fundamental equation. This paper introduces the damage theory to the fundamental equation of state-based peridynamic theory

and discretizes the fundamental equation

and then develops a corresponding peridynamic numerical program. Then classical fracture process of a single side tensional plate with a circle hole and the propagation and coalescence of cracks in rock under biaxial tensile stress are simulated using the theory. Numerical results from state-based peridynamic theory are in good agreement with those from RFPA2D. The results indicate that the state-based peridynamic theory not only breaks through the limitation of constant Poisson’s ratio on bond-based peridynamic theory

but also efficiently simulates the propagation and coalescence of cracks without any external fracture criterion. Therefore

the state-based peridynamic theory has great advantage over other numerical methods

and it can also provide a better understanding of propagation and coalescence of cracks.