In this work, we propose an innovative approach to investigate the admissibility of permutations to multistage interconnection networks—a challenging problem of switching theory. The proposed approach is centered upon modeling of multistage interconnection networks with colored Petri nets and use of Petri net analysis tools such as the unfolding technique and the invariants method. To assess the feasibility of the proposed approach we demonstrate that the complete unfoldings obtained in this work are polynomial in the problem size and employ an acyclic structure. The approach takes advantage of easy to use, yet extremely efficient, software tools.