Integrated　electricity　and　natural　gas　system　(IEGS)　plays　an　important　role　in　increasing　efficiency　of　energy　usage.　Uncertain　power　flow　calculation　is　helpful　to　system　optimization　and　scheduling　with　increasingly　prominent　uncertainty.　In　this　paper,　an　affine　energy　flow　algorithm　for　integrated　electricity　and　natural　gas　system　is　proposed　to　analyze　the　system　uncertainty.　First,　the　affine　models　and　energy　flow　equations　of　the　system　are　established.　Secondly,　the　prediction-correction　affine　energy　flow　algorithm　is　proposed.　The　algorithm　predicts　the　state　variable　according　to　the　sensitivity　analysis,　and　introduces　correction　coefficients　to　compress　the　predicted　state　variable.　At　the　same　time,　an　improved　decomposition　method　of　multi　energy　flow　is　adopted,　without　considering　the　calculation　order　of　multi　energy　flow　in　the　complex　coupling　network.　Finally,　the　case　simulation　verifies　the　advantages　of　the　affine　power　flow　method　in　conservatism,　computational　efficiency　and　tracking　the　source　of　uncertainty.　©　2023　IEEE.