A vibration damping device wherein a stopper rubber disposed between
opposing faces of a first mounting member and the retainer member so as
to project from one of the opposing faces to the other. When the first
and second mounting members undergoes relative displacement axially
towards each other, a shock produced at a time when an abutting face of
the first mounting member comes into contact with the open end face,
i.e., an abutting face of the retainer member absorbed by the stopper
rubber coming into contact with the other one of the opposing faces until
the first mounting member comes into contact with the open end face of
the retainer member. A receiving space is disposed between the opposing
faces of the first mounting member and the retainer member so that the
stopper rubber is accommodated in an elastically compressive-deformed
state within the receiving space when the abutting faces contact
together.