Abstract: The traditional interval energy flow algorithm of integrated energy system (IES) can only analyze the results of the combined action of multiple uncertainty factors, but fails to quantify the transmission process of each uncertainty factor and its influence on the system state variables. To deal with this issue, a system uncertainty model based on affine arithmetic is established and an affine multi-energy flow algorithm for integrated heat and electricity system (IHES) is proposed in this paper. First, an affine temperature transmission model is established based on the temperature exponential equation simplified by Taylor expansion, and further an affine model of the IHES is established considering the uncertainty of the conversion efficiency of the coupling elements. On this basis, considering the pipeline flow constraint, the heat network affine energy flow algorithm based on Back/Forward sweep method is proposed. Furthermore, the parallel iteration method for the affine energy flow of the IHES is proposed by taking the coupling element power as the boundary condition. Finally, based on the IEEE-33 system and 23-node heat network systems, the conservative advantages of the proposed method are verified; and the degree of influence of different node load variation on mass flow rate and temperature, and the interaction effects between subsystems are analyzed.