This paper describes a fully three-dimensional transient finite element method for calculating the flow behavior and fiber orientation during filling of injection molded parts. The fiber-fiber interaction is taken into account. The momentum and continuity equations are first solved with the viscoelastic stress treated as used body force. The kinetic equation for the orientation tensor is then integrated with known kinematics using the standard Galerkin method. The calculation is performed on a time-dependent flow domain. Since the method is truly three-dimensional, singular regions such as the pole front or near injection gates and solid boundaries, where decoupled approximations are not valid, are naturally dealt with. The material anisotropy behavior is modeled by using the Doi-Doraiswamy-Metzner model. Numerical results, involving the Poiseuille flow and the filling of an end-gated plate, emphasizing the importance of the three-dimensional coupling calculations between the flow and orientation are presented.