An inflatable housing includes bottom and side portions adapted to enclose a volume of atmosphere for use as an incubator or an oxygen tent. The side portions of the housing are constructed from spaced apart flexible sheets to form air chambers which extend over a substantial area of the side portions. When the air chambers are inflated, the side portions become self-supporting and the air chambers form a confined air barrier about the volume of atmosphere surrounding the patient. For safety purposes in certain embodiments, at least two independent air chambers are provided around the housing, each of the independent air chambers having the capacity when inflated to maintain the side portions in an upright position. In other embodiments, a top portion has an opening defined therein, with an air chamber ring disposed about the periphery of the opening. The air chamber ring when inflated is capable of maintaining the shape of the opening regardless of the state of inflation of the air chambers in the side portions.