A deck mounted pull riser tensioning system for a floating platform or vessel includes at least two cylinders having a cylinder body supported at an upper or lower end on a deck or tensioner support structure of the platform or vessel in spaced apart relation with the cylinder rods extending downwardly from the cylinder body, or vice versa. A load structure member is connected to lower ends of the cylinder rods or bodies and has an opening therethrough for receiving a portion of a riser extending from the seafloor. A vertically adjustable riser attachment supported on the load structure member over the opening attaches to a portion of the riser extending through the opening and generally centrally between the cylinders. The cylinders pull upwardly on the load structure member to exert an upward tensioning force on the riser at the location of the riser attachment.
