This shot gun butt was made with about 3/16 inch concave bow but sanded straight for a recoil pad. How do I restore it to a uniform concave for a a curved hard rubbre plate? Draw filing or sanding might work but would be so easy to get the tool to rocking and make the center line high. Thanking you for any ideas how to do this restore with more precision.

You said it. Filing and sanding. Then you fine fit the plate with inletting black and scrapers.

I am sure that you understand that there are a number of ways for you to accomplish the curve to the butt of a gun stock. The hand method using the correct tools requires a lot of time learning the skill though today the tools for the job are not of a reasonable cost also.
The non machine tool method is after drawing the profile each side of the blank a curved bottomed draw knife is used to do the initial rough shaping, cutting from the toe to the centre and the heel to the centre never cutting from the centre out. Or disaster will happen you will split the extreme outside wood along the grain. To produce the accurate curve and remove the draw knife marks a variable sole Compass Plane is used again from outside to centre. Bad news draw knives are not cheap to purchase and a Compass Plane is a mortgage for a good vintage one, and a little less for a modern version. I have used one but have never been able to justify the rather high cost to own one.
A drum sander that will fit in a DIY electric drill works well though the larger size drums and abrasive tubes for them are also not at all low in cost
So it is down to using a curved sole spoke shave and abrasive paper. I find sticking abrasive paper on large plastic bottles filled with sand works well for smoothing things off though can be heavy to use, when packed tight with sand though they keep their shape well. Whatever method you use always cut from outside to centre.

Thank you Mr. Dudley and Damascus for your reply.

I have a drum sander with dust collector that my talented father in law used for making decoys. I would sell it to anyone who would come to Gaithersburg, MD to inspect it. Includes a lot of paper and gosh knows what else that I just don't understand. Bill Murphy