The pylon of the present invention provides damping of vibrations transferred in both directions between the aircraft and the payload. That is, the pylon of the present invention damps the effects of aircraft vibrations on the payload as well as the effects of payload vibrations on the aircraft. This is accomplished in the present invention by substantially eliminating any rigid connection between the aircraft and the payload under normal operational conditions. Support of the payload is provided by a plurality of resilient suspension elements that are attached to both a base element and a payload interface element. The attachment is such that the payload element is suspended below the base element. Thus configured, the resilient suspension elements dampen the transmission of vibrations between the payload interface element and the base element.