The focus of this chapter lies on the influence of viscoelasticity on draw resonance. A linear stability analysis of all viscoelastic models considered in the previous chapter is presented, examining the influence of the Deborah number on the critical draw ratio, followed by a direct comparison and evaluation of the constitutive equations with respect to their stability predictions. The last section covers studies on the viscoelastic stability mechanism, including analyses of generalized Newtonian fluids and the influences of strain hardening and thinning effects.