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Three-dimensional finite element simulations were conducted for analyzing low velocity impact behavior of sandwich beams with a functionally graded (FG) core. After validating the finite element model using available analytical data, the effects of projectile initial velocity and kinetic energy, as well as the beam’s dimensions on the impact behavior and indentation and displacement history were studied. It was concluded from these observations that for sandwich beams having functionally graded cores, the maximum contact force increases and the maximum strain decreases compared to those of sandwich beams with a homogenous core.