[modal auxiliary] n (ca. 1904): an auxiliary verb (as can, must, might, may) that is characteristically used with a verb of predication and expresses a modal modification and that in English differs formally from other verbs in lacking -s and -ing forms
MODAL AUXILIARY
Meaning of MODAL AUXILIARY in English
Merriam-Webster English vocab. Английский словарь Merriam Webster. 2012