Abstract: Using the constitutive equation for slightly disturbed extensional flow^[10,11], an eigenvalue theory of stretching fluid sheets has been developed. The present stability analysis is given from the Lagrangean point of view. The dependent variables are written as functions of material particles and time. An equation for the amplitude of the disturbance stream function φ(η, t) is derived. A general eigenvalue theory is discussed to explain the instability of Newtonian and non-Newtonian stretching fluid sheets. For the non-Newtonian fluid case the theory is specialized to a Maxwell model. The present theory predicts the influence of wave number on the stability of stretching fluids.