There'a a similar question (How can something be "set in stone"?), but "cast" is a more specific verb than "set".
I was telling about Russian PM's famous malapropism "my words should be cast in granite" to an English speaker when I realized that "cast in stone" sounded rather natural. I checked, and this expression was present in both Collins and Macmillan dictionaries without any remarks about its usage.
You can cast something in metal, plaster or concrete, how did this verb stick to 'stone'? Is 'cast in stone' really a valid expression?