The capillary die flow of high density and linear low density polyethylenes is simulated under slip conditions to investigate the origin of sharkskin melt fracture. As suggested in the literature, it is shown that sharkskin originates at the exit of the die and is due to the acceleration (high stretching rate) of the melt as it exits the die. It is also shown that both adhesion and slip promoters eliminate surface defects by decreasing the stretching rate of the polymer melt at the exit region of the die. The effect of length-to-diameter ratio of the die on the sharkskin melt fracture is also examined. It is found that sharkskin is more pronounced in short dies which is in accord with experimental observations. Finally, it is suggested that applied pressure at the capillary exit suppresses surface defects.