Industrial pipelines are the safest, fastes and the most economical way to transport a large range of products, mostly those related to the oil industry. Pipeline systems are usually associated with huge financial investiments, being of fundamental importance to sustain their continuous operation, and maintainning them, reducing the number of interruptions or accidents at a minimum level. To accomplish that, pigs are used. Pigs are devices frequently used for many different purposes, a few of them are clemaming and dewatering a pipeline, sealing of a papeline, transport of different products, inspection and hydraulic tests all of them being accomplished without the interruption of the production lines. The developed model uses the unidimensional conservation equation of mass and linear momentum to simulate the transient movement of the fluid. The conservation of linear momentum of the Pig is also solved, Auxiliary equation to predict the by-pass flow is also incorporated into the system. several special cases are studied with very good results.