Based　on　the　potential　flow　theory,　the　hydrodynamic　pressure　governing　equation　of　an　incompressible　and　ideal　fluid　acting　on　a　single　oscillating　horizontal　cylinder　in　finite　water　depth　is　derived,　solved　using　the　variable　separation　method.　Analytical　solutions　for　the　hydrodynamic　pressure　of　the　oscillating　horizontal　cylinder　in　both　sway　and　heave　directions　are　established　via　the　multipole　expansion　method　and　verified　against　numerical　solutions.　Using　these　analytical　solutions,　the　hydrodynamic　pressure　distributions　of　the　horizontal　cylinder　under　sway　and　heave　motions,　varying　with　dimensionless　parameters　immersion　ratio　H　(H　=　h0/h)　and　diameter-depth　ratio　L　(L　=　2a/h),　are　studied.　It　is　found　that　at　the　distance　of　the　cylinder　from　the　free　surface　and　seabed　is　the　key　factor　influencing　hydrodynamic　pressure　distribution.　Additionally,　the　added　mass　was　calculated　through　integration　of　hydrodynamic　pressure,　and　the　variation　of　added　mass　coefficients　with　L　(L　=　2a/h0)　and　H(H　=　2a　/(h　-　h0))　is　analyzed.　It　is　observed　that,　in　both　sway　and　heave　motions,　added　mass　coefficients　increase　with　decreasing　L　and　increasing　H.　Simplified　calculation　formulas　for　added　mass　coefficients　of　the　horizontal　cylinder　under　sway　and　heave　motions　are　developed　using　a　two-step　fitting　method.　Finally,　errors　in　calculating　the　added　mass　coefficients　are　compared　between　the　simplified　calculation　formulas　and　the　analytical　solution,　showing　errors　of　less　than　5%,　indicating　high　accuracy　of　the　proposed　simplified　calculation　formulas　for　added　mass　coefficients.