In this study, shear flows of dry flexible fibres are numerically modelled using the discrete element method (DEM), and the effects of fibre properties on the flow behaviour and solid-phase stresses are explored. In the DEM simulations, a fibre is formed by connecting a number of spheres in a straight line using deformable and elastic bonds. The forces and moments induced by the bond deformation resist the relative normal, tangential, bending and torsional movements between two bonded spheres. The bond or deforming stiffness determines the flexibility of the fibres and the bond damping accounts for the energy dissipation in the fibre vibration. The simulation results show that elastically bonded fibres have smaller effective coefficients of restitution than rigidly connected fibres. Thus, smaller solid-phase stresses are obtained for flexible fibres, particularly with bond damping, compared with rigid fibres. Frictionless fibres tend to align with a small angle from the flow direction as the solid volume fraction increases, and fibre deformation is minimized due to the alignment. However, jamming, with a corresponding sharp stress increase, large fibre deformation and dense contact force network, occurs for fibres with friction at high solid volume fractions. It is also found that jamming is more prevalent in dense flows with larger fibre friction coefficient, rougher surface, larger stiffness and larger aspect ratio.