Numerical investigations of a full three-dimensional (3D) packing process and flow-induced stresses are presented. The model was constructed on the basis of a 3D nonisothermal weakly compressible viscoelastic flow model combined with extended pom-pom (XPP) constitutive and Tait state equations. A hybrid finite element method (FEM)finite volume method (FVM) is proposed for solving this model. The momentum equations were solved by the FEM, in which a discrete elastic viscous stress split scheme was used to overcome the elastic stress instability, and an implicit scheme of iterative weakly compressible CrankNicolson-based split scheme was used to avoid the LadyshenskayaBabuska Brezzi condition. The energy and XPP equations were solved by the FVM, in which an upwind scheme was used for the strongly convection-dominated problem of the energy equation. Subsequently, the validity of the proposed method was verified by the benchmark problem, and a full 3D packing process and flow-induced stresses were simulated. The pressure and stresses distributions were studied in the packing process and were in agreement with the results of the literature and experiments in tendency. We particularly focused on the effects of the elasticity and pressure on the flow-induced stresses. The numerical results show that normal stress differences decreased with incremental Weissenberg number and increased with incremental holding pressure. The research results had a certain reference value for improving the properties of products in actual production processes. (c) 2012 Wiley Periodicals, Inc. J Appl Polym Sci, 2012