A flow suppression device adapted to be connected to a high pressure fluid system includes an outer flow containment member of a porous and flexible construction. The outer flow containment member has an upstream end and a downstream end opposite the upstream end. The upstream end includes an inlet opening adapted to receive a flow stream of pressurized fluid from the high pressure fluid system and the downstream end being substantially closed. The flow suppression device also includes a primary inner flow containment member of a porous and flexible construction contained within the outer flow containment member. The primary inner flow containment member has an upstream end with an inlet opening adjacent the inlet opening of the outer flow containment member and a downstream end opposite the upstream end of the primary inner flow containment member.