A pressotherapy apparatus including a device for forming a treatment enclosure to be placed around a section of the body. The device has inflatable and deflatable cells having an upper membrane and a lower membrane which are connected together. The cells are supported by an external wall opposite a body surface of the device. The cells are disposed in a stack between two end cells. The cells between the end cells are stacked by overlapping in a position inclined between a high-end near to the external wall and a low end near to the body surface. The cells of the stack have an active portion of the upper membrane extending from the low end not covered by the lower membrane of an adjacent cell above.