Abstract: Recent studies show that the ductile fracture of some metals may depend on not only the stress triaxiality but also the Lode parameter. The MMC fracture criterion was developed in a recent publication incorporating the Lode parameter effect was implemented into ABAQUS and was then employed in the numerical prediction of the fracture behavior of 2024-T351 aluminum alloy Taylor rods. To reveal the effects of the stress state, parallel FE calculations were conducted by using another two fracture criteria (JC and BW) without incorporating the Lode parameter effect. These predictions were compared with experimental findings. The comparison shows that: JC fracture criterion calibrated by fracture data of axisymmetric rods under uniaxial tension overestimates the material's ductility and thus the simulations using JC fracture criterion underestimated the Taylor rod's fracture behavior. Simulations using BW fracture criteria predicted unreasonable fracture in the center of the projectile nose; Simulations using the MMC fracture criterion can give reasonable prediction of the fracture pattern.