Definition of shall modal verb from the Oxford Advanced American Dictionary

      

    shall

     modal verb
    modal verb
    NAmE//ʃəl//
     
    , NAmE//ʃæl//
     
     
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  1. 1(becoming old-fashioned) used with I and we for talking about or predicting the future This time next week I shall be in Scotland. We shan't be gone long. I said that I should be pleased to help.
  2. 2used in questions with I and we for making offers or suggestions, or asking advice Shall I send you the book? What shall we do this weekend? Let's look at it again, shall we?
  3. 3(old-fashioned or formal) used to show that you are determined, or to give an order or instruction He is determined that you shall succeed. Candidates shall remain in their seats until all the papers have been collected. Grammarmodal verbsThe modal verbs are can, could, may, might, must, ought to, shall, should, will, and would. Dare, need, have to, and used to also share some of the features of modal verbs.Modal verbs have only one form. They have no past or present participles and do not add -s to the 3rd person singular form:He can speak three languages. She will try and visit tomorrow.Modal verbs are followed by the infinitive of another verb without to. The exceptions are ought to and used to:You must find a job. You ought to stop smoking. I used to smoke, but I quit two years ago.Questions are formed without do/does in the present or did in the past:Can I invite Mary? Should I have invited Mary?Negative sentences are formed with not or the short form -n’t and do not use do/does or did:You shouldn't invite Mary. The error will not have affected our results.You will find more help with how to use modal verbs at the dictionary entries for each verb.
Grammarshall / willIn modern English, the traditional difference between shall and will has almost disappeared, and shall is not used very much at all. Shall is now used only with I and we, and often sounds formal and old-fashioned. People are more likely to say:I’ll (= I will) be lateandYou’ll (= you will) have your turn next.
See the Oxford Advanced Learner's Dictionary entry: shall