Several processes present free surfaces flows. Some of those processes go beyond engineering problems, including everyday issues like raindrops falling from the sky, water flowing down the river or through a faucet. In industry, extrusion and coating process are two examples of processes that are strongly affected by the behavior of the interface. The most commonly used free interface model was developed in the 19th century and describes as isotropic the behavior of interfaces and dependent on asingle parameter called interfacial tension. Since then, advances in the areaof interfacial rheology have been showing that the interfacial phenomena are more complex and accurate of more information to be modeled. In this line of thinking, this work analyzes the effect of interface viscosity on the dynamics of extrusion and slot coating process, in which the set of differential equations that governs the problem is solved by Finite Element method.