The nonlinear instability of the isothermal draw of optical fibers from cylindric preforms is studied. The unsteady model of the process is solved numerically, accounting for the effects of inertia, gravity and surface forces. The effect of viscosity and gravity on the nonlinear stability of the process is studied. The possibility of draw resonance occurring is shown for a rate ratio much lower than the critical one, obtained when solving the simplified model. The proposed solution can be used to study technological stability and to model the draw of fibers of other materials which behave as Newtonian fluids.