An　accurate　and　efficient　numerical　model　is　developed　to　calculate　the　earthquake-induced　hydrodynamic　pressure　on　uniform　vertical　cylinders　with　an　arbitrary　cross　section　surrounded　by　water.　According　to　the　boundary　conditions　and　using　the　variables　separation　method,　the　three-dimensional　Laplace　equation　governing　the　incompressible　water　is　transformed　into　a　two-dimensional　(2D)　Helmholtz　equation.　As　a　key　element,　a　circular　boundary　surrounding　the　structures　is　introduced　so　that　the　computational　domain　is　partitioned　into　unbounded　and　bounded　domains.　The　unbounded　domain　is　simulated　by　an　exact　artificial　boundary　condition,　which　is　derived　by　using　the　separation　variable　method.　The　impedance　matrix　of　the　entire　domain　is　obtained　by　the　finite-element　method.　The　hydrodynamic　forces　on　rectangular　and　round-ended　cylinders　are　calculated,　which　can　be　modeled　as　the　product　of　an　added　mass　of　water　and　the　acceleration　of　the　cylinder.　However,　these　complicated　expressions　of　the　hydrodynamic　forces　are　not　suitable　for　engineering　application.　Therefore,　simplified　formulas　for　the　added　mass　of　the　round-ended　and　rectangular　cylinders　are　obtained　by　the　curve-fitting　method.　The　results　indicate　that　the　precision　of　the　present　added　mass　formulas　is　enough　for　engineering　applications.