Vibration-damping composite body (10, 30, 50, 60, 70, 80, 120, 160, 182, 240) comprising a first elastic body (12, 32, 52, 62, 72, 82, 132, 162, 186, 224) and a second elastic body (14, 34, 54, 74, 84, 134, 164, 188, 232) which overlap one another, characterized in that the first elastic body (12, 32, 52, 62, 72, 82, 132, 162, 186, 224) is made of a material with a higher damping than that of the second elastic body (14, 34, 54, 74, 84, 134, 164, 188, 232), the first elastic body (12, 32, 52, 62, 72, 82, 132, 162, 186, 224) has a recessed part (18, 40, 56, 66, 76, 88, 138, 168, 226) which opens onto a surface of the first elastic body (12, 32, 52, 62, 72, 82, 132, 162, 186, 224), and the recessed part (18, 40, 56, 66, 76, 88, 138, 168, 226) forms a gap (22, 48, 58, 68, 79, 96, 142, 172, 236), and a
stress concentration part (28) configured to be subjected to
increased stress during a load action is placed on a wall of the gap (22, 48, 58, 68, 79, 96, 142, 172, 236) of the first elastic body (12, 32, 52, 62, 72, 82, 132, 162, 186, 224), wherein the first elastic body (12, 32, 52, 62, 82, 132, 162, 186, 224) and the second elastic body (14, 34, 54, 84, 134, 164, 188, 232) overlap in a direction of load action, and wherein the first elastic body (12, 32, 82, 132, 162, 186, 224) has a protruding part (16, 38, 86, 136, 166, 228) which is provided on an overlapping surface with the second elastic body (14, 34, 84, 134, 164, 188, 232) and protrudes towards the second elastic body (14, 34, 84, 134, 164, 188, 232), and the recessed part (18, 40, 88, 138, 168, 226) is formed on an outer periphery of the protruding part (16, 38, 86, 136, 166, 228).