There are two schools about how to class such stuff.
School A classes all of the below as auxiliary verbs
'be', 'do', 'have', 'will/would' 'shall/should', 'can/could', 'may/might', and 'must' are all classed as
auxiliary verbs.
School B
classes 'be', 'do', 'have' as
true auxiliary verbs, and
'will/would', 'shall/should', 'can/could', 'may/might', and 'must' as
modal verbs.
If you are interested in the differences between true auxiliaries and modals, visit
THIS SITE.
paco