We describe a robust numerical method for solving general flows of fibre suspensions that couples the CONNFFESSIT idea of Ottinger [H.C. Ottinger, Stochastic Processes in Polymeric Fluids, Springer, Berlin, 1996], and the DAVSS method of Sun et al. [J. Sun, N. Phan-Thien, R.I. Tanner, J. Non-Newtonian Fluid Mech. 65 (1996) 75-91; J. Sun, M.D. Smith, R.C. Armstrong, R.A. Brown, Finite element method for viscoelastic flows based on the discrete adaptive viscoelastic stress splitting and the discontinuous Galerkin method: DAVSS-G/DG, J. Non-Newtonian Fluid Mech., 1998, in press] The method does not require a closure approximation and allows good quality solutions at high volume fractions of fibres to be obtained. The algorithm was tested on the flow past the sphere in a tube problem, which forms the basis of the falling ball viscometry. The numerical results compare well with numerical the results from Phan-Thien and Graham [N. Phan-Thien, A.L. Graham, J. Rheol. Acta 30 (1991) 44-57] and the experimental data of Milliken et al. [W.J. Milliken, M. Gottlieb, A.L. Graham, L.A. Momdy, R.L. Powell, J. Fluid Mech. 202 (1989) 217-232].