The question that why punish the crime of attempt have discussed more than hundred years and have long occupied the imaginations of scholars of criminal laws. Actually, the issues involved are here the fundamental issues of theories of purpose of punishment and Unlawfulness. In order to understand the theoretical history of the issues and the Stand of today's discussion in Germany and U.S. as well as the focus shall be shifted toward and the possibility of development in the future, it is necessary to introduce and outline the history of theoretical challenges and developments of punishing the crime of attempt. This article discusses the concept and characteristics of attempting to commit an offense, and then analyzes the incapable attempted crime (impossible attempt). Finally, I argued that due to lake of formal and essential characteristics of a crime, attempt of imposibility is not a crime and should not be punished.