A pipeline pig support rack apparatus includes a frame having a plurality of supports mounted thereon, each extending upwardly from the frame. Each pipeline pig support includes clamps that are comprised of first and second u-shaped members that are attached with a hinge. A bolted connection opposite the hinge is provided for holding the u-shaped members together in a closed position when securing a pipeline pig. Lifting eyes on the frame are provided for enabling the frame, its pig supports and any contained pipeline pigs to be lifted as a unit. A basket receptacle optionally is provided that receives the frame. The frame and basket receptacle are each independently liftable. The basket receptacle prevents spillage of hazardous materials that might be residing upon the pigs after they have been used to clean a particular pipeline.