This article is concerned with vibration isolation, with antivibration mountings (resilient isolators), and with the static and dynamic properties of rubberlike materials that are suited for use in antivibration mountings. The design of practical antivibration mounts incorporating rubber or coiled-steel springs is described in Refs. 1–27; pneumatic isolators (air mounts, etc.) are described in Refs. 5, 28–35. Throughout the literature, as here, attention is focussed predominantly on the translational (vertical) effectiveness of antivibration mountings. However, the two- and three-dimensional vibration of one- or two-stage mounting systems is addressed in Refs. 4, 10, 12, 36–56. Following a description of the static and dynamic properties of rubberlike materials, the performance of the simple or one-stage mounting system is analyzed, account being taken of the occurrence of second-order resonances in the isolator and in the mounted item. In the latter case, as likely in practice, the bulk of the mounted item is assumed to remain masslike, whereas the feet of the item are assumed to be nonrigid (multiresonant). Discussion is then given to the two-stage or compound mounting system, which affords superior vibration isolation at high frequencies. Subsequently, the powerful four-pole parameter technique is employed to analyze, in general terms, the performance of an antivibration mounting with second-order resonances (wave effects) when both the foundation that supports the mounting system and the machine are nonrigid. The universally adopted method of measuring mount transmissibility is then described, followed by an explanation of how transmissibility can also be determined by four-pole parameter techniques based on an apparatus used by Schloss. The four-pole measurement approach has not been exploited hitherto, but it is apparently feasible and valuable because it enables mounts to be tested under compressive loads equal to those routinely encountered in service.