Damping is an important parameter for vibration control, noise reduction, fatigue endurance or impact resistance of composite materials. In this study, a micromechanical model was used to predict the damping of a composite material containing shear thickening fluids (STFs) at the fibre-matrix interfaces. Predictions of the model and dynamical mechanical analysis results are in concert. The damping of the composites was improved significantly. The dynamic properties exhibited a strong dependence on both frequency and applied external load amplitude. Damping peaks appeared which coincided with the thickening of the STF at the fibre-matrix interface. The location of the peaks depends on the onset of thickening and post- thickening rheological behaviour of the STF. This work shows that a micromechanics approach can be useful for an appropriate choice of microstructural design and properties of STFs in order to control the stiffness and damping behaviour of composites. STFs can be integrated at the microscale of polymer composites to create new materials with load- controlled adaptive dynamic stiffness-damping properties.