The die drool phenomenon, occurring as a result of the viscoelastic behavior of polymer melts during the flow, was experimentally investigated for metallocene-based LLDPE on a specially designed annular extrusion die with the capability to control the stress state at the end of the die by the help of a specific type of cooling system. With the aim of understanding the die drool phenomenon in more detail, the flow at the end of the die was analyzed theoretically by the finite element method employing a modified White-Metzner model as the constitutive equation. It has been revealed that negative pressure occurs at the die lip area, which seems to be an important factor driving the onset of the die drool phenomenon.