In this paper, an alternative solution algorithm for the creeping, 3D viscoelastic flow simulation is offered. It is based on the Parabolized Navier-Stokes Equations formulation (PNSE), which reduces the 3D problem to a sequence of 2D problems marched along a preferred direction (the dominant flow in the duct). This algorithm is extended to the limit Re approaching 0 (creeping flow) and the viscoelastic component of the extra-stress tensor that appears in the momentum equation is treated as a body force. The numerical results obtained with Criminale-Ericksen-Filbey (CEF) and Modified Phan-Thien Tanner (MPTT) models are compared against previous numerical and experimental data. As an application of the code, prediction of viscoelastic developing flow in channels is studied, since it is a common feature in many polymer processing applications, such as extrusion coating, film blowing, injection molding, and others in which there are confined flow in ducts after metering in extruder screw. The present algorithm offers a fast and efficient solution approach to the complex problem of 3D viscoelastic flow, allowing the detailed visualization of flow phenomena that would otherwise require significant computational resources. (c) 2005 Society of Plastics Engineers.