The pigging operation is a common practice in the petroleum and gas industry. Pigging flow lines is employed for many reasons including cleaning deposits such as wax layers, the removal of liquids and condensate, the separation of products pumped one after the other in the same pipeline, measurement, and control and flow line inspection. In this paper, the mathematical modeling of the transient motion of a pig through liquid and gas pipelines is presented. For this purpose, the fluid flow equations were combined with a linear momentum equation for the pig. The nonlinear equations are solved under an unsteady state condition by the method of characteristics (MOC) with a regular rectangular grid through the pipeline under appropriate initial and boundary conditions. From this simulation, the pig position, optimum flow rate in upstream flow and the time that the pig reaches the end of the pipeline are obtained. Comparison of the simulation results with the field data of liquid flow through the pipeline from KG to AG located in Iran show that the derived mathematical models are effective for the prediction of position and pig velocity under the given operational conditions of a pipeline. Similar results are also obtained for gas flow through the pipeline from Nar-1 to Nar-2 located in Iran, in comparison with the field data.