Are there any good alternatives to Linoleum and Wood for relief printing?
Anything you can cut into can be used to make a matrix for a relief print. Different materials have their peculiarities in terms of work process and result (compare linocutting to woodcutting), so it depends on what you are trying to achieve.

Here are some materials I've tried in the order I'd recommend them:


PLYWOOD
Pretty much like solid wood, comes in large sizes, cheaper than solid wood.
Note: There are different types of plywood, and they behave differently when cut. Choosing some soft wood to begin with may be a good idea.
HARDBOARD
Advantages: easy to cut, cheap, comes in large sizes
Disadvantages: produces a dusty mess, needs sealing, it is somewhat difficult to get fine detail
MDF
Same as hardboard, but a bit heavier
OSB
Advantages: cheap, comes in large sizes
Disadvantages: difficult to cut, easy to slip blade and cut yourself, dulls blades, does not work well with fine detail or on a small scale, heavy, easy to get splinters
Note: Unless you have nothing else to cut, it is really not worth it.