Petri Nets ( PNs) form a very useful model for procedures, organization and devices where information flows play an important role. They can represent the system at different levels of abstraction ranging from a single bit in a computer memory to the embedding of a computer system into its environment. Petri Nets make it possible to verify the system properties, as a result of their strong capability of modelling and analysing dynamic behaviour of the system at various levels of abstraction. In this paper, the reachability, marking and firing concepts of PNs are exploited to enumerate all spanning trees of a network. This has been achieved by assigning meaningful interpretation to the entities of the PN. A two-step method is proposed for the determination of all spanning trees of a network. In the first step all circuits of order < n -2 (n denotes total number of nodes of the given network) are generated and in the second step, all (n-1)-order combinations of transitions of a PN interpreted model of the network are retrieved which neither constitute a circuit nor contain any circuit generated in the first step. These combinations give precisely all spanning trees of the given network.