AbstractThe application of the penalty‐function formulation of the finite element method is made possible for analysing visco‐elastic fluid flows by the method which decouples the momentum and continuity equations from the constitutive equation. An upwind finite element scheme is combined with the method in order to solve the constitutive equation. As visco‐elastic fluid models, Jaumann derivative, upper and lower convected derivatives are considered. The Poiseuille flow and the flow through a plane converging channel are ana