Recent observations and events demonstrate that prisons serve as safe-haven for radicalization of the criminals and further development of terrorist networks. The traditional penitentiary system shows helpless when it comes to imprisonment of extremists. The article examines the problem of radicalization among the incarcerated in places of confinement. The author touches upon the following questions: What do radicalism, radicalization and deradicalization mean? How does radicalization take place? What stages does the process of radicalization flow through? What are de-radicalization measures taken by the governments? To what extent are these measures effective? The research demonstrates that while the traditional penitentiary system only exacerbates the process of radicalization of terrorists we still do not have a universally applicable and effective alternative yet.