The influence of anisotropic viscosity on fiber orientation evolution in classic squeeze flow is examined with a viscous fiber suspension of specified initial orientation state. The components of the anisotropic viscosity tensor for a well dispersed and collimated fiber suspension developed in micromechanical analyses earlier by one of the authors were combined in an orientation averaging approach to produce the effective suspension viscosity components for arbitrary orientation states. A coupled anisotropic viscosity constitutive relationship was numerically implemented into a displacement-based finite element code for nonlinear analysis of flow and fiber orientation. The numerical method was verified by agreement between predicted and observed responses for a single element subjected to canonical states of deformation. Evolution of fiber orientation during the deformation processes was confirmed by analytic predictions. This approach was validated by examining the squeeze flow of a fiber suspension studied earlier both analytically and experimentally. The present analysis was found to be in excellent agreement with experimental data and clearly demonstrated that evolution of fiber orientation and the resulting effective anisotropic viscosity tensor were essential to the correct predictions. (C) 2018 The Society of Rheology.