Is "May I have some drink?" incorrect?

Solution 1:

It's not ungrammatical. I would say though that "give me some drink" sounds either the request of a man in dire thirst, or who has a plan to be very drunk in short order, (or as an old-fashioned or regional usage) while "give me a drink" a less coloured request for a single beverage.

We do generally refer to individual beverages as drinks as a countable noun, and the liquids as drink as an uncountable. So likewise, "give me a beer" and "give me some beer" are both valid, but not identical.

I note that while "give me some drink" and "give me a drink" are both found in ngrams, the latter is more common, and this is a growing trend. Meanwhile, while it finds "can I have a drink" and "please give me a drink", it doesn't find the some equivalent of either.

Solution 2:

The difference is that drinks are things people consume in discrete units, unlike "food", "ice", and "sauce". You wouldn't say "can I have some ice cube".

Look at "sauce". This is both a countable noun and a mass noun in English. You can have two sauces but also some sauce. But if you wanted a sauce (a specific unit of sauce) or several sauces, you wouldn't say "some sauce". Similarly, if you want one drink or several drinks, you shouldn't say "some drink".

We generally reserve "some" for uncountables (some sand, some water) or plurals (some cars, some dishes).

If you want to be silly, you can argue that you were using "some" as an emphatic and what you really wanted was an exceptional drink.

(That's not to say it is incorrect or cannot be used. You just need a great degree of language skill. See Barrie England's answer for some examples that read well.)