The　uncertain　energy　flow　analysis　theory　is　important　for　planning　and　operation　optimization　in　integrated　heat　and　electricity　system　(IHES).　In　order　to　study　the　impact　of　uncertain　factors　on　the　IHES,　an　interval　multi-energy　flow　algorithm　based　on　affine　arithmetic　was　proposed　in　this　paper.　First,　taking　into　account　the　uncertainty　of　the　load　fluctuation,　an　electricity　affine　model　and　a　heat　affine　model　were　established　respectively.　Further,　considering　the　combined　heat　and　power　unit　and　heat　pump,　a　coupled　component　affine　model　was　built.　Moreover,　the　affine　energy　flow　of　the　heat　networks　based　on　Back/Forward　sweep　method　was　proposed,　based　on　this,　the　decomposition　iterative　of　the　affine　multi-energy　flow　was　further　proposed　of　IHES.　Finally,　the　completeness　and　conservativeness　of　the　proposed　method　were　verified　by　comparison　with　Monte　Carlo　simulation　method　and　interval　method　in　IEEE-33　electricity　network　and　23-node　heat　network　system.　The　impact　of　uncertain　factors　on　state　variables　were　analyzed　through　the　ability　of　affine　tracking　noise　symbols.　©　2022　IEEE.