"Barking mad" is an idiom used to describe someone who is completely insane or irrational. However, there are many other synonyms for this phrase that can be used to convey a similar meaning. Some other phrases that can be used instead of "barking mad" include "crazy as a loon", "out of one's mind", "mad as a hatter", "off one's rocker" or "nutty as a fruitcake". Each of these phrases has its own unique connotations but can be used interchangeably to indicate a person's eccentric or unusual behavior. When used creatively, synonyms for "barking mad" can add color and richness to any writing or conversation.