Kelly Cox writes about planing a 2mm "sag" into the soundboard of a bandura:

[snip]

>Using a #9-1/2 block plane (which has a 6.25" sole length) and assuming
that
>the belly of the bandura is 2 feet long, to produce a .080" 'sag' (which is
>roughly 2 mm) requires a set on your block plane of .005". Not
unreasonable!
>
>So the answer is, you should be able to plane the desired hollow with a
>standard block plane.

In theory this would work, but I'm not sure if it would in practice (I
know-- in theory there's no difference b/w theory and practice ).  I
think a simpler and less error prone approach would be to rough this out
using a toothing plane and scraper.   I know this is/was a common lutherie
technique for other thin-stock applications, and it should work for this as
well.

If you're set on using a plane, the Stanley #100-1/2 (tiny squirrel-tail
block plane with a rounded bottom) would do nicely for roughing out the
cavity.  I'd still finish off with a scraper, though.

I use the toothing plane and scraper combo all the time-- it allows you to
remove stock very quickly, while still retaining the high degree of accuracy
needed for thin stock preparation.

ralph