The non-linear magnetorheological behaviour is studied of a model system consisting of monodisperse silica particles suspended in a ferrofluid. The stress/strain curve as well as the flow curve was measured as a function of volume fraction silica particles and field strength, using a home-made magnetorheometer. Both curves were found to scale linearly with the volume fraction and quadratically with the magnetic moment of the silica particles. Affine deformation cannot lead to the observed yield stresses. Instead, a bead–rod model is described that gives results closer to what is observed experimentally. A master curve for the viscosity was obtained by plotting the dimensionless viscosity versus the Mason number, Mn. The free single chain model of Martin and Anderson does not give a good description of the measured curves. This may be due to the simplifications with respect to the microstructure of and processes in the suspension.