The stability of isothermal spinning of viscoelastic fluids which have strain-rate dependent relaxation time has been investigated using the linear stability analysis method. The instability known as draw resonance of the system was found to be dependent upon the material functions of the fluids like fluid relaxation time and the strain-rate dependency of the relaxation time as well as upon the draw-down ratio of the process. Utilizing the fundamental physics of the system characterized by the traveling kinematic waves, we also have developed a simple, approximate method for determining this draw resonance instability ; it requires oxy the steady state velocity solutions of the system in contrast to the exact stability analysis method which requires solving the transient equations. The stability curves produced by this simple, frost method agree well with those by the exact stability method, proving the utility of the method. The stability of other extensional deformation processes such as film casting and film blowing can also be analyzed using the method developed in this study.