The　resilience　against　displacement　revealed　asymmetrical　hysteresis　during　the　vibratory　compaction.　As　the　soil　compactness　was　high　enough,　the　jump　vibration　of　vibration　roller　was　produced.　An　asymmetric　hysteresis　model　was　established　in　terms　of　segmental　line　according　to　soil　property　parameters.　According　to　the　first　order　approximation,　the　equivalent　damping　coefficient　and　equivalent　stiffness　coefficient　were　deduced　through　the　harmonic　linearization　method.　By　means　of　numerical　simulation,　the　hysteresis　response　characteristics　of　the　drum　were　analyzed.　During　the　beginning　of　vibration　compaction,　soil　presents　elastic-plastic　characteristics　and　super-harmonics　occur.　With　the　increase　of　soil　density　during　the　ending　of　vibratory　compaction,　sub-harmonics　may　occur,　which　marks　the　occurrence　of　jump　vibration.　Under　some　conditions,　chaos　can　be　induced.　Adjustment　of　excitation　amplitude　and　excitation　frequency　can　availably　restrain　jump　vibration　and　chaos　motion　of　the　drum.