Flexible 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, eta, 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 phi(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 (gamma) over dot is also shown in the paper. (C) 2010 Elsevier B.V. All rights reserved.