I was shooting my Remington SPR22 double in a Benchmaster rest, and failed to note that the sling swivel in the toe was catching a lot of the recoil where the gun sits in the fork that holds the butt. As a result, the rear swivel broke off below the woodline. How on earth does one extract the broken shank?

Pick you up a broken screw extractor for that size screw. Drill a hole into the broken shaft the size the directions with the tool instructions say insert the extractor and then back out the screw.

Very carefully. You have to drill a hole into it and use an easy out. It could be something fairly simple, or, a nightmare. I have, on occasion, had to set the stock in the milling machine in order to square the broken shank to where I could get a clean, centered start with a smaller endmill.

If the stock is a working stock and not a show piece, you can mill and vaccuum the entire broken piece out and then make and fit an insert.

Gents: Thanks for the advice!

This is where a Dremal tool works good! Use the tiny engraving insert they sell and grind a slot across the brocken screw to the point a screw driver will fit and unscrew it. I've done this countless times on broken machine screws and so far all have came out. Helps to have some small screwdrivers also...