The fracture of ductile polymers occurs on the boundary between the molecular chain-oriented and non-oriented regions after the neck propagation. This behavior is caused by the concentration of craze that is a microscopic damage typically observed in polymers. In addition, it is known that the ductility of polymers decreases both at a high and a low strain rates in comparison with that at a middle one. In this paper, FE simulations are carried out for a crystalline polymer subjected to the tensile load at some strain rates by use of a homogenized molecular chain plasticity model and a craze evolution equation based on the chemical kinetics. Furthermore, failure criteria are proposed from an experiment on fibril strength. A fracture prediction based on the craze accumulation and the failure of fibrils is demonstrated applying the criteria to the numerical results. It is indicated that the fracture occurs at a smaller strain under a high and a low strain rate conditions than under a middle one.