The steady shear viscosity (?s), the steady first normal stress coefficient (?1), the steady second normal stress coefficient (?2), and extensional viscosity (?e) are four important parameters for polymer melts during polymer processing. In this article, we propose a stress and rate-dependent function to describe creation and destruction of polymer junctions. Moreover, we also introduce a movement expression to describe nonaffine movement of network junctions. Based on network theory, a nonaffine single-mode rheological model is presented for the steady flow of polymeric melts, and the equations of ?s, ?1, ?2, and ?e are derived from the model accordingly. Furthermore the dependences of ?s and ?e on model parameters are discussed for the model. Without a complex statistical simulation, the single-mode model with four parameters yields good quantitative predictions of the steady shear and extensional flows for two low density polyethylene melts reported from previous literature in very wide range of deformation rates. (C) 2012 Wiley Periodicals, Inc. J Appl Polym Sci, 2012