In this paper, the crack propagation and branching in the pre-cracked and notched samples have been modeled using nonlocal peridynamic theory. The bond-based peridynamic model has been numerically implemented which make it possible to simulate the various features of dynamic brittle fracture such as crack propagation, asymmetries of crack paths and successive branching. The fracture simulation of thin plates made of a brittle material with different crack and notch patterns has been considered. The molecular dynamics open-source free LAMMPS code has been updated to implement the peridynamic theory based modeling tool for two-dimensional numerical analysis. The simulations show that, the simulations time significantly decreases which is the core and distracting deficiency of the peridynamic method. Moreover, the simulated results demonstrate the capability of peridynamic theory to precisely predict the crack propagation paths as well as crack branching during dynamic fracture process. The good agreement between simulation and experiments is achieved.