The article studies some issues of modeling the synchronization of problems, using Petri nets. The features of synchronous and asynchronous models are shown. The dining philosophers’ problem is modeled with the help of Petri nets. The constructed model contains the idea of priority which helps to avoid possible deadlocks in the system. With the help of the Colored Petri Net, the well-known problem of synchronization about smokers is modeled, by whose means certain features of the Colored Petri Nets are revealed in relation to actions and semaphores. In addition, unlike the classical Petri Net, this network contains fewer transitions and positions, i.e., the amount of required memory is reduced.