In a separation membrane module in a module main body, an upper horizontal partition plate forms an upper fluid channel, a lower horizontal partition plate forms a lower fluid channel, a plurality of vertical outer tubes are fixed between the upper horizontal partition plate and the lower horizontal partition plate, and vertical tubular membrane elements extend through the respective outer tubes with a gap. An upper end of the gap is in communication with the upper fluid channel and a lower end of the gap is in communication with the lower fluid channel. An upper end opening of each of the membrane elements is open to outside of the module main body and a lower end opening each of the membrane elements is closed. A vertical partition plate is provided in either the upper fluid channel or the lower fluid channel to form an inlet chamber and an outlet chamber.