Furious, apoplectic, absolutely beside oneself with rage. (Imagine a rabid dog, foaming at the mouth and - wait for it! - barking...)
Can also refer to someone who is unbalanced (using "mad" in the British sense, referring to an insane person).
Synonyms for barking mad
On this page, you will find 30 slang terms related to barking mad. Some of the top words include: angryness, shiznit, postal, mad cracker, Bananas, and 25 more.