Foam compatible with resin will cost much much more than plywood.
We sell the foam and the plywood and everything else. We often say that
in small sizes, a foam sandwich boat will cost twice what a stitch and
glue boat cost.
Jacques from bateau.com

Old Nick wrote:
On Wed, 05 Jan 2005 03:43:20 GMT, Ookie Wonderslug

vaguely proposed a theory
......and in reply I say!:

remove ns from my header address to reply via email

What is the cheapest foam sheeting that one can buy that will not
melt when you apply polyester resin to it?

urethane. see below

What is the best source for
this foam?

hardware stores. glass shops

How much does it cost? Would it better than using luan as a
core?

No.!!!!!

First, unless you _want_ to build a boat (a desire will not argue
with) look at secondhand stuff, pro built. You will probably not pay
more than building, and should you be one of those fortunate souls
that can sell stuff you have, you will get more for it.

OK. Wood cores vs foam cores.

(1) For a small knockabout, use ply core. It spreads (resists point
loads; rocks, feet, jetties, etc) the load far more than any foam. If
the skin is damaged, it still keeps some shape. Kayaks are built from
ply or strip wood, because the result is more bump resistant/kg than
foam/glass. The wood actually has a structural part to play. For
larger boats it's different. They need stiffness and are less likely
to encounter point loads. Even there, there have been arguments.

(2) I mentioned urethane. Avoid that crap. It crumbles unbder stress.
The ONLY foam worth using in boats is expensive PVC foam. For cost
check out Airex/Klegecell. (Am I showing my age?) For a normal use,
biggish boat, you can't beat it. For a boat that is light and tough,
for rowing and knocking about (less than 20') use ply/glass.

The only _possible_ advantage for foam is that it will not rot. But a
fracture of the glass skin can cause major problems anyway. So....

(3) Boats on a budget are always a problem. Boating above all others
brings out the "weep once" feature.