This chapter presents the framework in which models of reduced dimensionality can be obtained for both the two-dimensional fiber drawing and the axisymmetric film casting configurations. The main assumptions are first introduced, followed by all steps necessary to derive the one-dimensional fiber and film models, starting from the two-dimensional mass and momentum conservation equations for isothermal and Newtonian fluids. The key feature is the use of an asymptotic expansion of the field variables based on the smallness of the aspect ratio of fibers and films. The derivations are made in a consistent way allowing to identify the main difference between both models, which only consists in a surface tension term, only present in the fiber model. The models are actually identical otherwise, safe the Trouton ratio, a constant prefactor entering into the extensional viscosity.