In this chapter, we investigate the influence of the reduction of width along the stretching direction, the so-called neck-in effect, on the draw resonance instability in Newtonian film casting problem using a linear stability analysis of a model of reduced dimensionality. We introduce the local Trouton ratio as a measure for the type of elongational deformation, which can be uniaxial, planar, or a combination of both. In the case of purely uniaxial or planar deformations, a one-dimensional model is sufficient. Additionally, the stabilizing mechanisms of the neck-in is revealed. Known alternative stability criteria are extended to the case of finite width and their validity is tested for finite aspect ratios.