The rheological model proposed by Leonov for a filled system was compared with experimental data. The experimental data included the steady-stare hear stress over a wide range of sheer rates, the transient stress in a start-up shear flow, stress relaxation after cessation of a steady-state shear flow, the step shear and the oscillatory shear flow at various amplitudes. In this model, total stresses are the sum of viscoelastic stresses arising from the micro-flow of polymer matrix around flocs of particles (matrix mode), and the stresses from particle-particle interactions (particle mode). The stresses in a matrix mode were modeled by a non-linear viscoelastic model [A.I. Leonov, Rheol. Acta 15 (1976) 85-98; A.I. Leonov, Rheol. Acta 15 (1976) 411-426]. The particle mode stresses were modeled by introducing a kinetic equation in the non-linear viscoelastic model which describes the processes of rupture and restoration of flocs of particles [A.I. Leonov, Rheol. Acta 34 (1990) 1039-1068]. Two different versions of this model are considered. The first model is based on the kinetic equation proposed by Leonov [A.I. Leonov, Rheol. Acta 34 (1990) 1039-1068] which is unable to fit experimental data over a wide range of shear rates. The second model is based on the kinetic equation proposed by Coussot et al. [P. Coussot, A.I. Leonov, J.M. Piau, J. Non-Newtonian Fluid Mech. 46 (1993) 179-217]. This model is capable of fitting the steady-stare shear viscosity data over a wide range of shear rates, and it is able to qualitatively describe the transient, and small amplitude oscillatory shear flow experimental data.