Rheological properties of non-Brownian straight and curved fibre suspensions in simple shear flow have been investigated by particle-level simulation. An inertialess fibre particle in Newtonian fluid is modelled as a collection of spheres connected with Hookean-type constraint force. The fibre motions are governed by hydrodynamic interaction based on Rotne-Prager correction to velocity disturbance and short-ranged repulsive force. An isolated curved fibre in simple shear flow shows a decrease in the period of rotation with increasing the curvature. Initial stress overshoot is observed as fibres undergo transition from isotropic orientation. Shear viscosity and first normal stress of straight fibre suspensions exhibit scaling with respect to concentration in a manner consistent with comparable literature results. The overall viscosity enhancement with increasing the curvature has been observed over the studied range of aspect ratio and concentration. This is accompanied by the decrease of flow-aligned component of configuration tensor. Straight and curved fibre simulation exhibits an average positive first normal stress difference but the data fluctuation is too large to distinguish curvature effect. (C) 2011 Elsevier B.V. All rights reserved.