GOLD!
Mummies had mummy masks to show what the person looked like in life.
Mummies that were pharaohs or otherwise royalty were buried with gold masks. Some mummies did not even get a tomb, because they were not wealthy enough to afford them.
if y "they" you mean the ancient Egyptians, then they made cat mummies/masks because they believed that cats were the sacred animal of the goddess Bastet or Bast. Bast was often moddled with a woman's body and cat head.
Cartonnage
cement
Most Japanese masks are made out of porcelain. It is because porcelain is a very shiny material.
The masks that were used as Egyptian "death masks" were usually made of gold and they had the purpose of was to give a dead face to the afterlife. The other masks were funerary masks. These were often made of wood and were made in to separate pieces.
sometimes but not likely
cartonnage
Flax or linen.
Flax or linen.