Flow-induced stress in compression stage is complex because compression flow combines both shear flow and extensional flow characters and involves the boundary change in melt front and compressing directions. To describe this kind of flow effectively, the theoretical model was established in terms of three-dimensional compressible and viscoelastic fluid, and the material derivative which includes mesh moving velocity was introduced to modify the convective terms in governing and constitutive equations based on Arbitrary Lagrangian Eulerian description. The corresponding variational equations were derived via Gauss formula and the finite element method was used to discretize the flow variables with mixed elements. In order to decouple the interdependence of velocity, stress, and temperature, a new approach involves twofold iterations was proposed to solve nonlinear flow problem. A new mesh updating scheme was presented to keep consistent with compressed regions. Numerical results indicate the compression can reduce the flow-induced stress significantly compared to conventional injection molding, increase compressing velocity enlarges flow-induced stress, and high temperature decreases flow-induced stress. The proposed method was verified by photoelastic pictures and measured pressures and temperatures during molding. POLYM. ENG. SCI., 56:287-298, 2016. (c) 2015 Society of Plastics Engineers