The mathematical model formalizes the solution of a problem of optimum control and it is meaningful to minimization of number of regional extremist system (bandit underground) taking into account relative importance of parts making it at the restrictions caused by "will" of the state to fight against extremism and objective dynamics of number of groups of extremists, an ethnosociocultural protestnost defined by factors (protest potential of society). The task was solved by means of imitating modeling on a method of scenarios.

Keywords: Mathematical model, method of scenarios, extremism, dynamics of number of groups of extremists, problem region, North Caucasus.