To illustrate a procedure for optimizing an industrial fiber spinning process through modeling, we make two choices: (1) we adopt the viscoelastic fiber‐spinning model of Denn, Petrie, and Avenas; and (2) we choose draw ratio as the process variable to be optimized. We begin with an analysis of the time‐dependent generalization of the Denn, Petrie, and Avenas model to determine all well‐posed boundary and initial conditions for this coupled system of nonlinear equations. Next we give thegeneralanalyticalsolutionto the steady dimensionless form of the problem, which we exploit to analyze the response of the solution toallpossiblesteady‐statevariationsin the dimensionless process parameters available within the Denn, Petrie, and Avenas model. We then predict both the conditions which optimize draw ratio in this model for the fiber spinning process, and how to achieve the maximum. This determination is first obtained in the dimensionless formulation and then transferred to the more practical dimensional formulation.