Sarcasm is a nuanced form of language where usually, the speaker explicitly states the opposite of what is implied. Imbued with intentional ambiguity and subtlety, detecting sarcasm is a difficult task, even for humans. Current works approach this challenging problem primarily from a linguistic perspective, focusing on the lexical and syntactic aspects of sarcasm. In this thesis, I explore the possibility of using behavior traits intrinsic to users of sarcasm to detect sarcastic tweets. First, I theorize the core forms of sarcasm using findings from the psychological and behavioral sciences, and some observations on Twitter users. Then, I develop computational features to model the manifestations of these forms of sarcasm using the user's profile information and tweets. Finally, I combine these features to train a supervised learning model to detect sarcastic tweets. I perform experiments to extensively evaluate the proposed behavior modeling approach and compare with the state-of-the-art.