A practical english grammar - Vyssaja skola 1978

The modal SHOULD
Sound symbols

a) Obligation, present or future (= ought to)

You should get some rest; you’ve been working very hard lately.

b) For those speakers who follow the. shall-will rule discussed earlier, should is used with subjects I and we when other speakers would use would.

I said I should see him the next day.

I should like to read that book.