A vibration damping device wherein: first and second mounting plate members (18, 20) configured to attach to respective components to be connected in a vibration damping manner are placed opposite to each other and connected by a main rubber elastic body arranged between opposing faces of the first mounting plate member and the second mounting plate member, the first mounting plate member is made in a shape of a rectangular flat plate, the second mounting plate member has a larger dimension in a longitudinal direction than that of the first mounting plate member, a first abutting portion and a second abutting portion rise from opposing sides of the second mounting plate member with respect to the longitudinal direction toward the first mounting plate member, a stopper plate has a central plate portion of a rectangular flat plate shape, the central plate portion is overlapped and attached on the first mounting plate member, first and second stopper portions (56, 58) are provided to a pair of opposing sides of the central plate portion of the stopper plate so as to limit an amount of relative displacement between the first and second mounting plate members (18, 20) by abutment against the respective first and second abutting portions (24, 26) which are provided to and integrally formed with the second mounting plate member, a dip part (56c, 58c) is provided so as to slope inward from a tip of a hanging plate part (56b, 58b) that extends from each of the first and second stopper portions (56, 58) provided to the respective opposing sides of the central plate portion of the stopper plate toward the second mounting plate member; and a pair of side plate portions each protruding toward the second mounting plate member are provided to another pair of opposing sides of the central plate portion of the stopper plate so as to extend continuously between the first and second stopper portions (56, 58) and close an opening to each side of the first and second stopper portions (56, 58) so that the pair of side plate portions are integrally connected to both edges of the first stopper portion and the second stopper portion in each width direction at both edges of the stopper plate in the longitudinal direction. first and second mounting plate members (18, 20) configured to attach to respective components to be connected in a vibration damping manner are placed opposite to each other and connected by a main rubber elastic body arranged between opposing faces of the first mounting plate member and the second mounting plate member, the first mounting plate member is made in a shape of a rectangular flat plate, the second mounting plate member has a larger dimension in a longitudinal direction than that of the first mounting plate member, a first abutting portion and a second abutting portion rise from opposing sides of the second mounting plate member with respect to the longitudinal direction toward the first mounting plate member, a stopper plate has a central plate portion of a rectangular flat plate shape, the central plate portion is overlapped and attached on the first mounting plate member, first and second stopper portions (56, 58) are provided to a pair of opposing sides of the central plate portion of the stopper plate so as to limit an amount of relative displacement between the first and second mounting plate members (18, 20) by abutment against the respective first and second abutting portions (24, 26) which are provided to and integrally formed with the second mounting plate member, a dip part (56c, 58c) is provided so as to slope inward from a tip of a hanging plate part (56b, 58b) that extends from each of the first and second stopper portions (56, 58) provided to the respective opposing sides of the central plate portion of the stopper plate toward the second mounting plate member; and a pair of side plate portions each protruding toward the second mounting plate member are provided to another pair of opposing sides of the central plate portion of the stopper plate so as to extend continuously between the first and second stopper portions (56, 58) and close an opening to each side of the first and second stopper portions (56, 58) so that the pair of side plate portions are integrally connected to both edges of the first stopper portion and the second stopper portion in each width direction at both edges of the stopper plate in the longitudinal direction.