The axisymmetric instability, which has a potential to cause bead formation along the fibers produced by electrospinning technique, is examined with the help of linear stability theory. The stability of a straight jet is analyzed under conditions corresponding to the electrospinning of two types of polymeric fluids, the PIB-based Boger fluid with low electrical conductivity and the highly conductive PEO solution in ethanol/water. For the former, the rheology is described by the Oldroyd-B model, suitable for unentangled polymers under weak elongational flow. On the other hand, the highly conductive polymer solution experiences a strong elongational flow due to very high axial electric force, for which the viscoelasticity is appropriately described using the extended Pom-Pom (XPP) model, the nonlinear rheological model for entangled polymeric systems. Contrary to previous studies, which oversimplifies the electrified jet as a cylindrical jet with uniform radius and other jet variables, we analyze the stability of the realistic non-uniform thinning jet as observed in electrospinning experiments. The stability of the thinning jet profile, obtained using the 1D slender body model, is examined by imposing non-periodic axisymmetric disturbances and constructing the spectrum of disturbance growth rate. The thinning jet is found to be relatively less unstable than the uniform jet, which is attributed to the stabilizing role of extensional stresses, in addition to the axial variation in surface charge density and electric field, present in the non-uniform deforming jet, but ignored in the analysis of the uniform jet. For both the reference fluids considered, the polymer addition renders the jet stable and thus, suppresses the bead formation during straight jet path of electrospinning. Also, the enhancement in fluid elasticity, characterized by the flow Deborah number, plays a stabilizing role for the thinning jet of Oldroyd-B fluid. However, for the XPP fluid, the fluid elasticity shows a rich behavior with a stabilizing effect for moderate values of Deborah number, attributed to stretching of polymer chain between the branch points, and a destabilizing effect for highly elastic fluids, due to strain rate softening. Increasing the strain hardening effect in the polymer solution, achieved by increasing number of arms at the branch point in the XPP molecule, tends to stabilize the electrospinning jet against axisymmetric disturbances potentially producing smooth bead-less fibers. While the instability in low conductivity fluid is driven by capillary forces, the instability in highly conductive fluid is an oscillatory conducting mode driven by the coupling of the surface charges and the axial electric field. (C) 2017 Elsevier Ltd. All rights reserved.