An　accurate　frequency　domain　model　is　proposed　to　analyze　the　seismic　response　of　uniform　vertical　cylinders　with　arbitrary　cross　section　surrounded　by　water.　According　to　the　boundary　conditions　and　using　the　variables　separation　method,　the　vertical　modes　of　the　hydrodynamic　pressure　are　firstly　obtained.　Secondly,　the　three-dimensional　wave　equation　can　be　simplified　to　a　two-dimensional　Helmholtz　equation.　Introducing　the　scaled　boundary　coordinate,　a　scaled　boundary　finite　element　(SBFE)　equation　which　is　a　linear　non-homogeneous　second-order　ordinary　equation　is　derived　by　weighted　residual　method.　The　dynamic-stiffness　matrix　equation　for　the　problem　is　furtherly　derived.　The　continued　fraction　is　acted　as　the　solution　of　the　dynamic-stiffness　matrix　for　cylinder　dynamic　interaction　of　cylinder　with　infinite　water.　The　coefficient　matrices　of　the　continued　fraction　are　derived　recursively　from　the　SBFE　equation　of　dynamic-stiffness.　The　accuracy　of　the　present　method　is　verified　by　comparing　the　hydrodynamic　force　on　circular,　elliptical　and　rectangle　cylinders　with　the　analytical　or　numerical　solutions.　Finally,　the　proposed　model　is　used　to　analyze　the　natural　frequency　and　seismic　response　of　cylinders.　©　2021,　The　Author(s).