A heat integrated distillation column (HIDiC) is a new and highly energy-efficient distillation process. In the present work, multiple steady-states in HIDiC are analyzed. In HIDiC, the pressure in the rectifying section is kept higher than that in the stripping section by using a compressor to enhance beat transfer from the rectifying section to the stripping section through the wall. Therefore, an energy balance, particularly the influence of the compressor, must be taken into account for the analysis. In this research, two types of operation policies are investigated: P1) constant compressor power and P2) constant pressure ratio. First, the conditions for making multiple steady-states are derived on the basis of the first principle model of the HIDiC. Then, the analysis results are validated through simulations. The results show that: 1) the instability condition depends largely on the compressor operation policies; 2) in case PI, multiple steady-states appear when the top product is highly pure, the bottom product is relatively impure, vapor now rate is large, and compressor power is small; 3) in case P2, multiple steady-states appear when the bottom product is highly pure; and 4) multiple steady-states appear in a wider range of operation in case P2 than in case P1.