A magnetic brake with a solid iron cylinder rotating at high speeds is considered, The rotor iron is both conductive and permeable. The magnetisation curve is non-linear. Special attention is paid to the correct integration of the angular velocity term. A Newton-Raphson scheme dealing with the non-linear material characteristics is applied The numerical oscillations appearing in the finite element model at high velocities are overcome by all adaptive mesh refinement technique combined with the artificial diffusion upwind technique. Did effects due to the finite length of the rotor are incorporated by an electric circuit coupling. Simulations are performed to study the influence of the saturation of the moving rotor upon the speed-torque characteristic of the magnetic brake. It is remarkable that in the case of this solid rotor magnetic brake, the saturation of the rotor iron has a beneficial influence on the device performance.