From Longman Dictionary of Contemporary Englishapartment blockaˈpartment ˌblock British English, apartment house American English, apartment building noun [countable] 
TBBa large building containing many apartments
TBBa large building containing many apartmentsExamples from the Corpus
apartment block• Damian got out, his arm around Domino, and they ran into an apartment block.• A quiet street and the beard stood in the shade of an apartment block doorway.• Accordingly, he had indeed doubled the surveillance team, detailing two men to each side of the Eldorado apartment block.• This time she took him to a room in a large apartment block set near factories and oil-storage tanks.• Marina's is an old apartment block on Putnik Street. 