Foam board behaves like a light, waterproof timber: it saws, routs, drills and takes a screw, and it does not swell when the shop front leaks. It is the default for cut-out lettering, display panels, shelf risers and short-run interior fit-out.
Thicker sheets stay flat over larger spans; thinner sheets are cheaper but will bow if you hang them from two points. Tell us the span and the fixing method and we will specify the thickness.

