A vibration-attenuating coupling device for use with two rigid members one of which is subject to vibrations produced by, for example, an internal combustion engine installed on an engine driven vehicle, characterized by a laminar vibration absorptive structure composed of a main resilient member fitted to the rigid member subject to vibrations and at least one auxiliary resilient member smaller in spring constant and secured between the main resilient member and the rigid member to be isolated from the vibrations transmitted to the other rigid member.