In this chapter, we introduce the linear stability analysis for the particular configuration of infinite-width film casting and in the purely viscous case. Note that this configuration is identical to the fiber drawing one with neglecting surface tension, as demonstrated in Chap.  2 . Next we present an equivalent formulation that includes the normal stress difference as additional dependent variable. This alternative formulation offers a more general framework for the extension of the purely viscous case to incorporate all additional effects such as gravity, inertia, surface tension (for fiber drawing), neck-in (for film casting), viscoelasticity, and non-isothermal effects that will be considered in the rest of the book. Two methods to solve the eigenvalue problems resulting from the linear stability analysis are then presented, namely the Chebyshev colocation and the continuation methods, discussing the advantage and inconvenience for both. The last section gives more insights on the physical mechanism of the draw resonance instability and presents alternative criteria for the critical draw ratio based on kinetic wave theory.