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The peridynamic theory was first introduced, then 2 examples of high-speed crack propagating and branching phenomena were given and investigated. The effects of peridynamic parameters including the neighbourhood radius and the grid spacing, and such external parameters as the material elastic modulus, the material density and the temperature difference, on the crack propagating velocity and the crack branching angle were analyzed. It is found from the numerical results that the crack propagating velocity decreases and the crack branching angle increases with the neighbourhood radius; both the crack propagating velocity and the crack branching angle decrease with the grid spacing; the crack branching length in the material of a smaller elastic modulus and a larger density is longer; the crack propagating velocity increases with the elastic modulus difference; the crack propagating velocity increases as the materials'density difference decreases, and decreases with the temperature difference. Moreover, the crack propagating and branching process can be simulated with the peridynamic method spontaneously, without any outer criterion and preset crack propagating paths. Therefore, peridynam-ics has natural advantages in the simulation of high-speed crack propagating and branching phenomena. [ABSTRACT FROM AUTHOR]