This　first　part　of　a　two-part　paper　on　the　John　A.　Roebling　suspension　bridge　(1867)　across　the　Ohio　River　is　an　analytical　investigation,　whereas　Part　II　focuses　on　the　experimental　investigation　of　the　bridge.　The　primary　objectives　of　the　investigation　are　to　assess　the　bridge＇s　load-carrying　capacity　and　compare　this　capacity　with　current　standards　of　safety.　Dynamics-based　evaluation　is　used,　which　requires　combining　finite-element　bridge　analysis　and　field　testing.　A　3D　finite-element　model　is　developed　to　represent　the　bridge　and　to　establish　its　deformed　equilibrium　configuration　due　to　dead　loading.　Starting　from　the　deformed　configuration,　a　modal　analysis　is　performed　to　provide　the　frequencies　and　mode　shapes.　Transverse　vibration　modes　dominate　the　low-frequency　response.　It　is　demonstrated　that　cable　stress　stiffening　plays　an　important　role　in　both　the　static　and　dynamic　responses　of　the　bridge.　Inclusion　of　large　deflection　behavior　is　shown　to　have　a　limited　effect　on　the　member　forces　and　bridge　deflections.　Parametric　studies　are　performed　using　the　developed　finite-element　model.　The　outcome　of　the　investigation　is　to　provide　structural　information　that　will　assist　in　the　preservation　of　the　historic　John　A.　Roebling　suspension　bridge,　though　the　developed　methodology　could　be　applied　to　a　wide　range　of　cable-supported　bridges.