English makes use of modal verbs (a type of auxiliary verb) to express attitude or perspective. In academic writing, modal verbs are used in a number of ways

1. Modal verbs for ability  - can, could
2. Modal verbs for possibility  - may, could, can, might
3. Modal verbs for obligation - should, must, have to, cannot
4. Modal verbs for necessity - need, must

Ability

Can and cannot are often used to express ability in the present;

• Smoking can lead to serious illness, such as lung disease or cancer.
• Dogs cannot see colours as well as humans do; they are red-green colour blind, having only two types of cone cells at the back of their eye.

Be able to + infinitive can be used instead of can

• Researchers have been able to quantify the observable changes in social structure over time.

Could or could not are often used to express ability in the past:

• Einstein could never accept quantum theory as a complete theory.

Possibility

In academic writing, writers may need to be cautious in the way they present ideas (this is known as hedging). One way of expressing uncertainty is to use the modal verbs may, could, can or might.

• Less severe allergy reactions may also occur, including rash and upset stomach.
• ... provide an extensive list of all terms that may be used, indicating three-letter abbreviations for each.
• In the next week, a proposed skate park could be given the go-ahead by the council.
• Social care services can play a key role in challenging such ageism.
• Not to mention the possibility that the machine might register the votes incorrectly.
• An adrenal mass might also be a cancer of the adrenal cortex.

Obligation

Modal verbs such should, must, have to and cannot are used to express obligation. 

• Judges should not assume that juries will understand the reasons for giving shorter prison sentences.
• Courts must never abdicate their duty to protect citizens from the abuse of power by governments.

Necessity

The verb need is a semi-modal. It is a normal verb which is used as a modal verb. It uses the auxiliary verb do to form the negative and it is followed by a noun phrase or to + base form.

• Users will need Abode Acrobat to view these files.
• Cotton is a naturally absorbent material that does not need to use chemical absorbers.

Often, the noun form need is used with for + noun phrase or to + base form).

• This approach makes use of most people's ability to determine sharp focus for themselves, minimizing the need for highly trained and scarce personnel.
• There is a need to explore new approaches.
• There is a need to build bridges between this type of learning and formal, accredited learning.

Past Modals

Some (not all) modal verbs can be used in the past tense by adding have + 3rd form.

• The hands are held over the stomach, suggesting that it might have been used for stomach pains.
• The ancient Egyptians can't have travelled to America.