In one embodiment, a container with an overpressure safety device comprises a wall having a depression in at least a portion of the wall that expands when the pressure inside the container exceeds a predetermined level. The container further comprises a clamp bridging over the depression and restraining the angular expansion of the depression, while at the same time enabling the depression to expand radially. As a consequence, the outer dimensions of the container remain essentially constant when the pressure inside the container exceeds the predetermined level. The container may be tubular in shape and the depression may be shaped like a groove extending parallel to the longitudinal axis of the container, while the clamp may be shaped like a bar affixed to the outer wall of the container in two or more points spaced angularly on opposite sides of the depression.