Summary Chart of Past Modals

MODAL	MEANING	EXAMPLE
Could have (+ past participle)	possibility impossibility disbelief	I could’ve ordered dessert, but I was already full. I couldn’t have married her because neither of us wanted to move to another country. How could you have thought I would accept such a foolish excuse?
May/Might have (+ past participle)	possibility (may or might) suggestion	We didn’t tell her the truth, because we were afraid or hurting her feelings. However, she may have suspected that we weren’t telling her the truth. He might have tried to be more cooperative. In that case, his coworkers would have been more likely to help him.
Should have/Ought to have (+ past participle)	expectation regret or judgment about past action	She ought to have called by now, since it’s 8:15 and she said she’d call by 7:30. I know I should have told her the truth. (But I didn’t and I regret it.)
Must have (+ past participle)	conclusion	He must have taken my grammar book home. I accidentally picked up his book, and I guess he took mine.
Would have (+ past participle)	Preference Unfulfilled wish	I would rather have gone to the park, but she wanted to see a movie. I would have liked a cookie, but there weren’t any in the house.

Past modals are often used to express unfulfilled or unrealized actions or events. The past modals can also be used in progressive and passive verb constructions.

Modal + progressive: You should have been keeping all of your work in a folder.

Modal + passive: Your work should have been kept in a folder.