We study the effect of viscoelasticity on the fluid dynamics of slot coating flow of dilute polymer solutions. The fluid is modeled by the Oldroyd-B and FENE-P equations in a conformation tensor formulation. The fully coupled equations of the flow are solved by the DEVSS-TG finite element method together with the elliptic domain mapping method to capture the unknown free surface. We observe that dilute solutions, where the presence of polymer molecules affects the flow field, behave qualitatively differently from ultra-dilute solutions, where the presence of polymer molecules does not alter the flow field. In dilute solutions: (1) the stagnation point on the free surface moves towards the static contact line and the recirculation zone shrinks with increasing Weissenberg number; (2) once the stagnation point reaches the static contact line, the hoop stress on the free surface changes sign from negative to positive, which destabilizes the flow; (3) the region of most severe polymer stretch and distortion also moves to the static contact line. The field variables, such as velocity, velocity gradient and conformation tensor, become singular due to a geometric singularity at the static contact line which leads to the failure of the computational method. In contrast, in ultra-dilute solutions, the computations fail when the mesh can not capture steep stress boundary layers at the free surface. The low-flow limit of inertialess slot coating flow is examined in terms of the Elastocapillary number; the coating window for uniform coating narrows as the liquid grows more elastic. (c) 2007 Elsevier B.V. All rights reserved.