The determination of the rocking state for an isolation structure is a fundamental issue to estimate the safety of the isolat? ed layer under a seismic excitation. In this study， by using the tensile deformations at the vertical direction of the rubber support in the isolated layer， the rocking states of the isolation structure are divided into ones with unuplifting， uplifting， and rocking. A clas? sification method is then proposed for estimating the rocking state of the high-rise structure with isolated layer. Inspired by the influ? ences of the aspect ratio （AR）， vertical yield-weight ratio （αv ）， horizontal yield-weight ratio （αh ）， vertical cycle （Tv ）， horizontal cycle （Th ）， system damping ratio（η） to the swing response of isolation structures under seismic excitation， boundary spectrum of isolation structures is achieved. It shows that swing response decreases with the increase of αv，Th and η（the effect of Th is most sig? nificant）， which is beneficial to the control of the sway response as well； swing response increases with the increase of AR and Tv （the effect of Tv is most significant）， which is not conducive to the control of swing response， and the most advantageous measure to control the swing response is increasing Th， decreasing Tv.