The　seismic　response　of　offshore　structures　is　generally　influenced　by　water-structure　interaction.　This　study　focuses　on　the　earthquake-induced　hydrodynamic　forces　on　axisymmetric　offshore　structures.　Based　on　the　finite　element　method,　an　accurate　and　efficient　time-domain　numerical　model　for　simulating　water-axisymmetric　structures　subjected　to　horizontal　earthquakes　is　developed.　First,　according　to　interface　boundary　condition　and　using　the　method　of　separation　of　variables,　the　three-dimensional　(3D)　wave　equation　governing　the　compressible　water　is　transformed　into　a　two-dimensional　(2D)　governing　equation　in　the　vertical　and　radial　directions,　where　the　solution　in　the　circumferential　direction　is　analytical.　Secondly,　an　exact　artificial　boundary　condition　(ABC)　in　frequency　domain　is　developed　by　using　the　separation　of　variables　method.　Third,　a　high-accuracy　ABC　that　is　local　in　time　but　global　in　space　is　obtained　by　applying　the　temporal　localization　method.　Furthermore,　the　high-accuracy　artificial　boundary　condition　is　discretized　and　coupled　with　the　finite　element　equation　of　the　near　field,　leading　to　a　symmetric　second-order　ordinary　differential　equations.　Finally,　the　coupled　finite　element　equation　for　the　water-axisymmetric　cylinder　is　presented.　The　proposed　method　is　used　to　study　the　effect　of　water　compressibility　on　the　seismic　response　of　and　evaluate　the　seismic　responses　of　a　composite　bucket　foundation.