As process capabilities become more advanced, the need to predict flow phenomena at a smaller scale increases significantly. Viscoelastic secondary flows in square ducts were simulated using a finite volume approach. Single mode and multimode Giesekus and Phan-Thien Tanner (PTT) models were implemented and were able to reproduce full three-dimensional (3D) flow through a square duct. Results for low density polyethylene (LDPE), polystyrene, and polycarbonate are all in agreement with experiments [Dooley, Viscoelastic flow effects in multilayer polymer coextrusion, PhD Thesis, Technische Universiteit Eindhoven (2002)] as well as numerical results using a finite element method (FEM) and a meshless radial function method (RFM), [Lopez et al., SPE ANTEC Tech. Pap. (2010)]. The mathematical model presented here has shown the potential to model full 3D flow in more complex geometries. POLYM. ENG. SCI., 2012. (C) 2012 Society of Plastics Engineers