Based　on　the　derived　in-plane　equations　of　motion　for　inclined　cables　in　the　global　secant　coordinate　system,　the　modified　Irvine　equations　are　deduced,　which　compensates　the　limitation　of　Irvine　equations　in　calculating　the　in-plane　natural　vibration　of　inclined　cables.　Compared　with　the　exact　results　obtained　by　a　Galerkin　method,　it　is　shown　that　the　modified　Irvine　equations　can　be　used　to　calculate　the　in-plane　natural　frequencies　and　modal　shapes　of　inclined　cables.