you would have to use 8-3.
you are correct in that 10-3 NM is limited to 30 amps

Thanks for the reply.

Just to be clear ('cause I'm not sure I was): The NEC specifies that a 10-3 copper conductor is capable of handling 40 amps, but only if the insulation is rated at 90 degrees C (see the table at http://en.wikipedia.org/wiki/American_wire_gauge for instance).

I know the insulation in NM-B cable is rated at 90 degrees C, but the specifications of the cable I have says that the ampacity of the cable must be limited to the rating at 60 degrees C, which is indeed 30 amps (thanks for confirming; I was knee deep in a torn out kitchen at the time).

So, I guess a follow up question would be, is there any 10-3 NM-B cable that I could connect to a 40 amps breaker, one that doesn't have the ampacity limit at the 60 degree rating? Or, conversely, why does the NEC state that a 10 ga. wire can handle 40 amps when the insulation is rated at 90 degrees C, but the wire manufacturer says to limit ampacity to the 60 degree limit?

Here is a link that might be useful: Wire Chart

You won't find any connections that are rated at 90úC so you can't use that column.

The 90 column in table is only useful if you need to take derating into account. As Joed points out, for most purposes you're stuck with the 60.

Thanks, guys. I pulled out the old 10-3 NM and put in 8-3 NM-B. I always wondered about that column, as in why it was there if no one made a connector that could handle that heat.

Learn something new every day.

A secondary (or perhaps tertiary) issue to consider is whether you really want to waste electricity heating the wires in the walls rather than the food that you're cooking. When you're on the high end of the wire's ampacity, upsizing conductors a size can be worthwhile, kind of like adding more insulation to your attic.