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In this paper, application of so-called eigenproblem in extremal algebras are studied. The motivation is to model a system of user roles. The eigenproblem is a task of finding such vectors, which are transformed to their multiple (or remain unchanged) by a given space transformation. The formal tools used in extremal algebras are similar as the matrix operations in linear algebra, only the standard operations+ and* are substituted by maximum and minimum, or by other binary operations. Matrix multiplication is then performed formally in the same way as in linear algebra. Investigation of the eigenproblem in max-min algebra is important for applications connected with questions of system reliability or with fuzzy relations. For special types of matrices such as circulant matrices, the computation can often be performed in the simpler way than in the general case. This article was based on project of user roles called “Connection of system for identity management for algorithms for the analysis of access privileges and modeling of user role within the innovation project” which was carried out by company AG COM C. in collaboration with the University of Hradec Kralove, together operating in association HIT cluster. The base of the project is to develop algorithms applicable to the analysis of access rights and modelling user roles from the state of the permission settings to the final systems.