When someone is impersuadable, it means that they are unwilling or unable to be convinced or influenced. There are several synonyms for this word that convey a similar meaning, including stubborn, unyielding, obstinate, unrelenting, inflexible, unresponsive, and uncompromising. These words all suggest a level of resistance to persuasion or change. Other synonyms for impersuadable include immovable, rigid, unbending, unshakeable, and obdurate, which indicate a firmness in one's position that is difficult to sway. Regardless of which term is used, the meaning remains the same--these individuals are not open to persuasion or change, and are often viewed as being difficult or uncooperative.