The two-dimensional flow of fiber suspensions in a straight channel is numerically studied by using a rheological model for anisotropic fluids. The fibers are assumed to be rigid cylindrical bodies with negligible inertia. Considering the suspension as a homogeneous medium, the orientation field is described by a fourth-order tensor which relates velocity gradients to bulk stresses generated by the fibers. The orientation evolution equation for the fourth-order orientation tensor is implemented using a sixth-order quadratic approximation that satisfies the required tensorial symmetry. The final form of the equations presents a convenient and tractable model for spatially nonuniform flows.