Service is the process of meeting needs through the activities of others directly. Service is usually synonymous with queues, and queues are what many people complain about. Most of the taxpayers complained about the queues, indirectly they would blame the poor service because of the queues that had piled up. Queues can be reduced by improving services, while one way to improve services is to analyze services using the Petri Net model. Petri Net is mathematical modeling for discrete event systems. Petri Net can be used to model and analyze algebraic problems of transportation networks, manufacturing systems, telecommunications networks, parallel process systems, and so on. In this study, a Petri Net Model of the annual vehicle tax payment service system was created as many as 16 places, 14 transitions, 2 operators, and 30 arcs using WOPED 3.2.0 software. The length of time for tax payment services for taxpayers who have completed the file is faster with a total time of 27 minutes compared to those who have not completed the file with a total time of 35 minutes. The Petri Net model of the annual type of vehicle tax payment service system can be presented in the form of a backward incidence and forward incidence matrix which is used to see the queuing pattern at Samsat Oku Timur 1 with a mathematical model. Columns in the backward incidence matrix can be used to determine which transitions are enabled.