BAN family of logic is used to analyze the security of cryptographic protocols. Five logics in the BAN family of logic are analyzed, including GNY, AT91, MB, SVO and BAN logic itself. Many defects of BAN family of logic are presented, including some defects found in research. A model is presented to describe the BAN family of logic first. And then the defects of BAN family of logic are classified according to this model. Some problems concerning BAN family of logic are presented in order to stimulate further research.