Resource allocation is crucial in the distributed systems. It is a key step in designing the mechanisms of systems for determining the resource allocation mechanism, it is important for obtaining the desired efficiency in the system, plus it is vital for predicting and preventing Deadlocks. Various models of Petri Net (Stochastic PN, Colored PN, Generalized PN, etc.) are used for modeling, simulation, execution, and solving the problems of resource allocation. SAN models are used for modeling the problems pertinent to resource allocation. First, we shall address the basic concepts pertinent to these models and the resource allocation problem (introduction chapter), then, some applications of the Petri Net and SAN models in the distributed computational systems or systems based on them shall be studied. Finally, the issues and findings will be concluded.