A side air bag is disclosed for a motor vehicle, and takes the form of a three-dimensional airbag which is formed from two super-imposed layers of fabric. The super-imposed layers of fabric, when laid flat, have a substantial common area of super-imposition. Infill pieces formed from either at least one gusset forming insert or from a portion or portions of fabric of one or both of the fabric layers which extend beyond the area of super-imposition are provided. The air-bag has an inflatable region towards the upper part of the air-bag and an inflatable region towards the lower part of the air-bag. The two inflatable regions are separated by a part of the air-bag which is constrained when the air-bag is inflated, to have a thickness less than the thickness of either of the said regions.