Viscoelastic FENE and PTT constitutive models are considered in the simulation of high-speed reverse roll coating flow with polymeric paint solutions, where wetting lines and air-entrainment are incorporated. Both FENE-CR and FENE-P models are utilised to illustrate the influence of shear-thinning in the context of strain-hardening properties. Strain-softening is introduced via PTT solutions in contrast. Steady solutions are derived numerically through a time-stepping hybrid finite element-finite volume sub-cell algorithm with dynamic free-surface location, drawing upon a fractional staged, predictor-corrector, and semi-implicit time-stepping procedure. A systematic computational and rheological study allows for parametric variation in elasticity (Wi-variation), level of strain-hardening (A(L)), shear-thinning and solvent fraction (beta). Various problem aspects are investigated to reveal the influence of viscoelasticity on vortex developments, pressure and lift profiles, shear and strain-rates, and critical stress states. Specific features of viscoelastic flow response are observed by analysing stress and flow structures over a range of Weissenberg numbers. The novel aspects of the work lie in the application of the algorithm to the reverse roll coating process under such viscoelastic fluid models. (C) 2014 Elsevier B.V. All rights reserved.