Machinery or instruments are subjected to external forces from a base in many cases. It can have a negative influence on manufacturing accuracy, tightness, wear of machine parts, work safety etc. Therefore, it is necessary to perform suitable passive elastic bearings of machinery to eliminate external vibration from the base. An application of suitable vibroisolating materials is one way of the vibration elimination. The aim of the paper is to study vibration damping properties of different materials by means of a non-destructive method of forced mechanical oscillations. Different factors influencing transfer damping of mechanical vibration were investigated in this work, e.g., material type and its thickness, excitation frequency of mechanical oscillations, size of mass load and effect of material composition. These factors were subsequently evaluated. Finally, suitable recommendations for passive damping of mechanical vibration were described.