The paper presents measurement and results of mathematical modelling of damping in cyclic loaded magnetorheological composites - MRC. The original experimental set-up for cyclic shearing mode has been created. Examples of possible applications, measurement and processing mechanical signals (shear stress - T, deformation - g) and magnetic signals (strength of magnetic field - H) were provided. For the modelling four-parameters viscoelastic-viscoplastic model was chosen. Result of identification confirmed an appropriate choice of the model.