A tool for extracting well pipe casings resembles an enlarged pipe-thread tap. The tool is designed to be suspended under and driven by the traveling rotary table and hydraulic vertical drive system of a conventional drilling rig. By this means, well pipe casings are withdrawn from wells by engaging the tops of such well pipe casings, and unlike the prior art, which grapples well pipe casings at their very bottom, and at the end of a cable. Unlike withdrawing casing by a cable pull, wherein cables stretch and unstuck casings might launch like projectiles, the extractor tool manages to withdraw well pipe casing in a recoilless manner, which is more controlled, and safer.