During　the　five-axis　flank　milling　process,　the　uncut　chip　area　varies　continuously　with　the　cutter　motion,　which　leads　to　a　challenging　issue　for　the　geometric　construction　of　the　instantaneous　uncut　chip　thickness　(IUCT).　In　this　paper,　a　novel　approach　to　calculate　the　IUCT　effectively　considering　the　cutter　runout　effect　is　proposed.　The　element　motion　of　the　cutter　extracted　from　the　cutter　location　file　(CLF)　is　described　with　one　linear　variable　and　two　angular　variables,　which　are　necessary　factors　in　the　IUCT　calculation　of　five-axis　milling.　The　geometry　relationship　between　cutter　motion　and　IUCT　has　been　analyzed,　and　the　parametric　expression　of　IUCT　in　five-axis　milling　can　be　deduced　to　predict　the　cutting　force.　The　explicit　five-axis　IUCT　expression　facilitates　a　more　comprehensive　understanding　of　the　key　parameters　in　the　cutting　process,　which　could　be　helpful　in　optimizing　the　processing　parameters.　Compared　to　the　numerical　method　based　on　true　tooth　trajectories,　the　time　consumption　of　the　proposed　method　is　reduced　greatly　in　the　simulation.　The　experiment　of　five-axis　flank　milling　is　carried　out,　and　the　result　reveals　that　the　presented　method　can　be　well　applied　to　the　practical　milling　process.　We　believe　that　the　IUCT　model　in　this　paper　will　promote　the　simulation　and　optimization　system　in　five-axis　machining.　©　The　Author(s),　under　exclusive　licence　to　Springer-Verlag　London　Ltd.,　part　of　Springer　Nature　2024.