Upper　story　rigidity　of　base　isolated　structures　Is　smaller,　and　the　isolated　structure　bears　a　bigger　vertical　load,　a　multi-story　rubber　pad　is　adopted,　the　total　thickness　of　the　rubber　bearing　is　bigger　and　it　has　not　only　an　obvious　horizontal　but　also　vertical　displacements.　It　causes　the　upper　storys　to　produce　swing.　The　vibrations　and　the　control　equations　of　a　base　isolated　structure　with　swing　are　derived,　analyzes　the　swing　＇　s　influences　to　the　vibration-control　of　the　base　isolated　structure　are　analyzed.　The　conclusions　obtained　from　above　analysis　suggest　that　the　swing　may　have　some　influences　to　the　vibration-control　of　the　isolated　structures.　The　rotation　rigidity　and　damping　ratio　of　the　base　isolated　structure　and　superstructural　vertical　load　obviously　influence　the　vibration-control　of　the　base　isolated　structures　with　swing.