The interaction of moving expansion waves with junctions of branched duct is theoretically studied. Two cases of the interaction are studied both analytically and numerically. One is the interaction of expansion waves with a single junction. The other is the interaction in the case of a double junction. As an analytical approach, a quasi-steady flow model is utilized. As a numerical approach, the method of chracteristics is used. The strengths of the transmitted and reflected waves are shown for many different combinations of the cross-sectional areas and the angles of the side branches and the strengths of incident expansion waves. The numerical results show clealy how transmitted and reflected waves develop with time in the transient process of the interaction.