Fiber formation of polymeric materials is an industrial relevant process that involves shear, extensional, and elastic material response. The polymer solution is compressed and sheared in a die and then exhibits die swell, a predominantly elastic response, as the fibers are extruded. Computational fluid dynamics (CFD) models are needed to describe these flows, to inform process design and perform process optimization. However, CFD of viscoelastic flows have both increased complexity and increased computational costs compared to Newtonian flows, since a polymer stress constitutive equation is necessary to describe the polymer rheology and must be solved as a separate equation. These stress-constitutive equations introduce a symmetric tensor unknown to the CFD calculation. Furthermore, constitutive equations that perform well in shear such as an Oldroyd-B model, become undefined at high extension rates. In this paper, we investigate die swell of polymeric solutions where the free surface location must be determined as part of the numerical solution. The viscoelastic equations are discretized using DEVSS-G method with both LBB and bilinear elements for the velocity and pressure spaces and bilinear interpolation for the stress and velocity gradient space. A multimode Phan-Thien-Tanner (PTT) constitutive equations is used for the viscoelastic response. An arbitrary-Lagrangian-Eulerian (ALE) implementation with pseudo-solid mesh motion is used to solve for the location of the free surface. The velocity, pressure, stress, and velocity gradient equations are discretized and solved with a finite element method. A kernel transformation of the conformation tensor for the stress equations is used to improve stability of the method as the fluid elasticity is increased [1,2]. Die swell data is available for several fluids, with varying viscosities, elasticities, and shear and extensional thinning. These data compare favorably to the numerical solutions. ACKNOWLEDGMENTS SNL is managed and operated by NTESS under DOE NNSA contract DE-NA0003525 REFERENCES [1] Balci, Nusret, Becca Thomases, Michael Renardy, and Charles R. Doering. "Symmetric factorization of the conformation tensor in viscoelastic fluid models." Journal of Non-Newtonian Fluid Mechanics 166, no. 11 (2011): 546-553. [2] Varchanis, S., A. Syrakos, Y. Dimakopoulos, and J. Tsamopoulos. "PEGAFEM-V: a new Petrov-Galerkin finite element method for free surface viscoelastic flows." Journal of Non-Newtonian Fluid Me