A microstructure oil-damping shock absorber was designed for the protection of electronic-packaging components in vibration-impact environments. The nonlinearity of the oil viscosity, the oil flow characteristics, and the coupling between the oil and the physical structure were included in a mathematical model of the oil-damping shock absorber to attenuate vibrations. The results of multi-parameter-coupled dynamic tests show that the mathematical model accurately simulates the actual physical system of the oil-damping shock absorber. The model could be used for engineering designs of vibration-impact isolation of electronic-packaging components.