An inflatable device for blocking a chimney flue or other duct is in the form of a plastics bag 1 having an inflation tube 2 that opens through the wall of the bag 1 into a flexible, tubular sleeve 4 that is sealed circumferentially to the bag-wall at each of its opposite ends 5,6 within the bag 1. The sleeve 4 is vented into the bag 1 via diametrically-opposed apertures 7 mid-way between its ends 5,6 so that on inflation of the bag 1 the sleeve 4 limits distention of the bag 1 longitudinally of the sleeve 4 to a flatish form. The bag 1 is constructed of two plastics sheets 8,9 that are sealed together in a peripheral rim 10 with the two ends 5,6 of the sleeve 4 sealed centrally to the two sheets 8,9 respectively, and with an open end of the inflation tube 2 sealed through the bag-wall centrally within one end 5 of the sleeve 4. The rim 10 of the bag 1 is bowed inwardly to allow for limited ventilation of the otherwise-blocked chimney flue or duct.