A pad or cover for an air bag assembly formed of a thermoplastic elastomer and having an outer wall that includes a substantially H-shaped thin-walled breaking seam designed to break when the air bag is actuated. The breaking seam is H-shaped, as viewed in a vertical direction, and the cover includes an ordinary portion outside of the breaking seam. A horizontal seam portion of the substantially H-shaped portion has straight line portions respectively connected to two vertical seam portions lying on both left and right sides of the substantially H-shaped configuration and a curved U-shaped portion that is interposed between the straight line portions. The thickness of the ordinary portion at the outer peripheral side of the U-shaped portion is thicker than the thickness of the ordinary portions in the vicinities of intersections between the vertical seam portions and the straight line portions.