'Shall' is a modal verb that is used to indicate future action or intention, often in the first person. It is commonly used in British English and may sound more formal than 'will' when used to indicate future action. In addition to indicating future action or intention, 'shall' can also be used to make an offer or invitation, or to ask for advice or instructions. Take a look at the following examples:

'Should' is a modal verb that is commonly used to give advice, suggest a course of action, indicate obligation or duty, express probability or expectation, or indicate hypothetical or conditional situations. Have a look:

'Shall' is commonly used in official documents and formal contexts to indicate obligations and requirements, particularly when discussing legal or mandatory actions. 'Should', on the other hand, is used to offer advice or recommendations or suggest a course of action, particularly in situations where there is some degree of flexibility or discretion. The choice between 'shall' and 'should' depends on the level of obligation being conveyed. For example:

'Should' can be used to talk about assumptions or expectations in certain contexts. When used in this way, 'should' can indicate a likelihood or probability based on what is considered normal or expected. Have a look:

'Shall' can be used with first-person singular or plural pronouns 'I' and 'we' to make offers in a polite or formal way. When used in this way, 'shall' can help to convey a sense of politeness and respect, particularly in formal or professional settings. Take a look at the examples:

In general, 'shall' is considered to be a more formal and traditional modal verb, while 'should' is considered to be less formal and more common in everyday speech.
'Shall' is often used in legal or official documents to indicate requirements or obligations, and can convey a sense of authority or seriousness.
In contrast, 'should' is often used to give advice or make suggestions, and can convey a sense of informality or friendliness.

We can create negative sentences with 'shall' and 'should:'
To do so, you simply add 'not' to the modal verb as illustrated below:

Take a look at these examples for clarification:

We can create yes/no questions and wh-questions with modal verbs including 'shall' and 'should.'

To make yes/no questions, we put the modal verbs at the beginning of the sentence followed by the subject and the main verb. For example:

To create wh-questions, we start by a wh-word such as what, when, where, who, why, and how followed by a modal verb, the subject, and the base form of the main verb. For instance:

'Should' can be used with the second type of conditionals. This type of conditionals is concerned with hypothetical situations with a low chance of occurrence. When 'should' is used in these sentences, 'if' is removed and the subject and modal verb are inverted. Have a look: