What are "modal-verbs"?

Solution 1:

The modal verbs are a subset of the "verbs of being", which are properly called auxiliary verbs. The classical modal verbs are:

• shall
• should
• will
• would
• may
• might
• must
• can
• could

Modal verbs are peculiar in that they have no infinitive form (you can't say to shall) and cannot be combined with other modal verbs in Standard English (you can't say I will might go).

By way of contrast, the other auxiliary verbs are formed from be, have, and do, and they don't have these properties. You can say to be, and you can combine a non-modal auxiliary with a modal: I should have bought those shoes.

For more detailed discussion, see Wikipedia.