As　a　flexible　forming　progress,　single　point　incremental　forming　(SPIF)　has　excellent　forming　limit　over　traditional　forming.　Based　on　SPIF,　the　introduction　of　an　energy　field　like　ultrasonic　vibration　(UV)　is　an　interesting　method　that　could　further　improve　the　formability　of　materials.　However,　there　are　few　theoretical　explanations　for　the　role　of　UV　in　SPIF.　Thus,　a　failure　model　which　considers　the　UV　effect　has　been　developed　to　evaluate　the　forming　limit　in　UV-assisted　SPIF.　A　truncated　cone　part　was　formed　using　A1060　and　Cu-Al　sheet　for　verification.　The　performance　of　the　theoretical　model　is　confirmed　by　comparing　with　experimental　results,　and　the　mechanics　of　formability　variation　in　UV-assisted　SPIF　have　been　explained　through　the　theory　of　surface　effect,　including　vibration　effect　and　heat　effect.　The　influence　of　process　parameters　on　the　formability　of　both　materials,　such　as　amplitude　and　feed　rate,　is　also　analyzed.　Meanwhile,　the　states　of　equivalent　plastic　strains　and　tress　triaxiality　at　fracture　location　are　discussed　in　SPIF　with/　without　UV　and　Nakajima　test.　The　proposed　model　and　method　are　expected　to　provide　a　benchmark　and　its　scientific　interpretation　of　the　UV　effect　in　SPIF.　©　The　Author(s),　under　exclusive　licence　to　Springer-Verlag　London　Ltd.,　part　of　Springer　Nature　2025.