It is an object is to improve the cleaning effect, to reduce the cleaning time, and to reduce the consumption of cleaning water during cleaning of an inside of an ink chamber of a flexographic printing machine. For cleaning an ink chamber 20, purge air “a” is supplied from pipes 46a-b to the ink chamber 20, and an ink “f” is collected from an ink supply pipe 26 and an ink recovery pipe 36 to an ink can 30. Subsequently, cleaning water “w” is supplied from the pipes 46a-b to the ink chamber 20, as well as defining a cleaning water circulatory passage 44 constructed from a three-way valve 24, an ink supply port 22, the ink chamber 20, excessive ink recovery ports 32, the ink recovery pipe 36, and a connecting pipe 40 for circulating cleaning water “w” through the circulatory passage 44 to clean inside the ink chamber 20. At the same time, compressed air “a” is supplied from a compressed air supply pipe 424 of an air gun 42 to generate bubbles in the cleaning water “w”, thereby improving the cleaning effect on the ink chamber 20 by the agitating action and the turbulent flow generating action of the bubbles.