Modal verbs are a subset of helping (auxiliary) verbs. One might wonder what modal verbs help us do. The answer to that is that modal verbs help English speakers to express probability, ability, obligation, advice, permission, and habits. These are the so-called primary meanings of modal verbs.In their secondary function, the modal verbs (except shall) can be used to express the degree of certainty/uncertainty or probability.

1. Secondary functions
of Modal verbs
must can may
should needn’t

2. Positive logical assumption
She must be on holiday
(I’m sure she is)
He must be working.
(I’m sure he is working)
He must have been on
holiday.( I’m sure he has been ..)

3. Negative logical assumption
She can’t be her mother.
( I’m sure she isn’t)
She can’t be sleeping.
(I’m sure she isn’t sleeping)
She can’t have come back.
( I’m sure she hasn’t come back)

4. Supposition doubt
She may visit you tonight.
( Perhaps she will visit , I’m not sure)
She might be cooking now.
( Perhaps she is cooking now)
He might not have left yet.
(Perhaps he hasn’t left yet)

5. Criticism of a past action
He should have told her
the truth. (She didn’t tell the truth. It
would have been better if she had told
the truth)
You ought to have tried
harder. (…but you didn’t, so your
team lost)

6. Possibility in the past
Yesterday, there was a
terrible accident. The driver
could have been killed. (It was
possible, luckily it didn’t happen.)

7. Possibility in the past
The lights are still on.
Helen might have
forgotten to turn them off.
( It was possibly true…)

8. Absence of necessity (past)
You needn’t have bought
me a gift. ( It wasn’t necessary for
him to buy her a gift, but he did)
He didn’t need to wash
the car. (It wasn’t necessary for him
to wash the car so he didn’t.)