Page 358 - Practical English Usage 3ed - Michael Swan, Oxford

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After modal auxiliary verbs, we use the infinitive without to of other verbs. Ought is an exception - see 403.
I must water the/lowers. (NOT } 1IUtSt t6 fUtlter ...}
Progressive, perfect and passive infinitives are also possible (see 280).
I may not be working tomorrow.
She was so angry she could have killed him.
The kitchen ought to be painted one of these days.
Modal verbs do not have infinitives or participles {t6 may, mttying, m.t:tyeti do not exist}, and they do not normally have past forms (though would, could, should and might can sometimes be used as past tenses of will, can, shall and may). Other expressions are used when necessary.
I'd like to be able to skate. {NOT ••• t6 etlR skate.}
People really had to work hard in those days. (NOT Pe6fJle really flll:I:Stetl
1:116'* . . . )
However, certain past ideas can be expressed by a modal verb followed by a perfect infinitive (have + past participle).
You should have told me you were coming. I think I may have annoyed Aunt Mary.
For details of these uses, see the entries on particular modal verbs.
Modal verbs have contracted negative forms (can't, won't etc) which are used in an informal style. (Shan't and mayn't are only used in British English; mayn't is very rare.) Will and would also have contracted affirmative forms (,il, 'd). For details, see 143. Some modals have both 'strong' and 'weak' pronunciations. For details, see 616.
There is quite often used as a preparatory subject with modal verbs, especially when these are followed by be (see 586).
There may be rain later today.
meanings
We do not normally use modal verbs to say that situations definitely exist or that particular events have definitely happened. We use them. for example. to talk about things which we expect. which are or are not possible, which we think are necessary. which we want to happen. which we are not sure about. which tend to happen, or which have not happened.
He may arrive any time.
She could be in London or Paris or Tokyo - nobody knows. I can't swim.
I think you ought to see a lawyer.
We really must tidy up the garden.
What would you do ifyou had a free year?
Edinburgh can be very cold in winter.
I think they should have consulted a doctor earlier.
You might have told me Frances was ilL
For further general information about the meanings of modal auxiliary verbs. see next section. For more detailed information. see the sections for each verb.
modal auxiliary verbs: introduction 353
page 326