In the present study, the flow of a fibre suspension in a channel containing a cylinder was numerically studied for a very low Reynolds number. Further, the model was validated against previous studies by observing the flexible fibres in the shear flow. The model was employed to simulate the rigid, semi-flexible, and fully flexible fibre particle in the flow past a single cylinder. Two different fibre lengths with various flexibilities were applied in the simulations, while the initial orientation angle to the flow direction was changed between 45° ≤ θ ≤ 75°. It was shown that the influence of the fibre orientation was more significant for the larger orientation angle. The results highlighted the influence of several factors affecting the fibre particle in the flow past the cylinder.