An issue that is essential to contemporary society is the question of state security and personal safety of the citizens. Therefore, the state has to deal with one of the most important threats, i.e. radicalization. The phenomenon of home-grown radicalism is known in Western European countries. The phenomenon of radicalization should not be identified solely with contemporary domestic Islamic terrorism. Radicalism is not limited to one ideology. The question about the process of acquiring extremist beliefs is one of the most important for political scientists, political psychologists, sociologists and criminologists. Wanting to deal with the etiology of the decision about a terrorist attack, the focus should be on the moment when potential terrorists start and undergo the process of radicalization. The article aims to signal the problem of radicalization in Polish penitentiary units. The authors do not provide the knowledge necessary to counteract this phenomenon in penitentiary units. However, they point to the definition problems, the theoretical model of radicalization, the place of radicalization in the European Union's policy. They also present the penitentiary unit as a place susceptible to radicalization. They formulate general remarks on combating radicalization among prisoners. They inform that the Prison Service should not be left alone in counteracting the radicalization of prisoners. It is an element of the state security system. It also cooperates with other entities in the rehabilitation of prisoners. The authors acknowledge that the way to prevent the negative effects of the radicalization process of prisoners is first of all training personnel in this field. It is also the fundamental issue to isolate prisoners who are a source of danger. In this area, the authors suggest that if the radical attitudes of prisoners are intensified, it is worth considering introducing legislative solutions facilitating faster and adequate operation of prison staff in such cases.