a b s t r a c tFlexible fibre suspensions in a Newtonian fluid experimentally show shear-thinning and normal stress differences in steady state. This paper discusses properties of the shear viscosity, Á, and the first and second normal stresses, N 1 and N 2 , using the help of direct fibre simulation based on PSM (particle simulation method), considering near-field hydrodynamic interactions, collision without attractively interacting forces and friction forces between fibres. The software reproduces the tendencies obtained experimentally such as shear-thinning and decreasing N 1 . In addition to this result, when the aspect ratio is low (<10) and the volume fraction varies between v = 0.05 and 0.1, shear-thickening and increasing N 1 are predicted. These tendencies are analyzed using the orientation of the end-to-end vector and the radius of gyration. The prediction of N 2 as a function of˙ is also shown in the paper.