The film-flow problem in dip coating is simulated numerically for non-Newtonian fluids based on Carreau-Yasuda (CY) and Herschel-Bulkley (HB) constitutive equations, with particular focus on coating-film-thickening phenomena and on the evolution of free surface and flow field under different sets of conditions. Finite element method (FEM) is combined with remeshing technique using a commercial code (Polyflow). Numerical predictions of the final film thickness and free surface for HB and CY fluids are successfully compared with experiments under the given conditions. Results show that the combination of FEM-remeshing technique could be useful for dip-coating design and optimization. Effects of coating fluid properties and withdrawal speed on film thickening and free surface shape and location are also discussed. Flow fields under different conditions are presented to analyze the evolution of the entire flow field and flow characteristics in detail. (C) 2016 Society of Plastics Engineers