A numerical method to simulate fibre suspensions in shear how is reported, which takes into account short range interaction via lubrication forces and long range interaction via slender body approximation, together with an appropriate Ewald summation technique. The numerical results are averaged to produce macroscopic properties of the suspension, including the Folgar-Tucker diffusion constant, the structure functions, and the reduced viscosity. In the semi-concentrated to concentrated regime, the fibres no longer follow Jeffery＇s orbits, they align mostly with the shear direction. Numerical data on the diffusivity constant, the structure functions, and the reduced viscosity agree reasonably well with available experimental data.