Electrospinning is a novel process that allows the production of nanoscale fibres by using electrostatic force to accelerate a fluid jet. During electrospinning, it has been seen that axisymmetric instabilities can occur, giving rise to beaded fibres as the product of spinning. In the current paper we investigate these instabilities. Our model couples the laws of electrohydrodynamics with equations for polymeric rheological behaviour. In addition, a linear stability analysis is performed which allows the unstable axisymmetric modes to be identified. In the current work we focus on the stability of solutions with high electrical conductivity such as PEO/water systems. For solutions of low electrical conductivity (such as PIB Boger fluid systems) it is seen that the axisymmetric instabilities are driven by capillary action, whereas for higher conductivity solutions the driving forces are more complex, and involve the interplay between the electric field and the viscoelasticity of the charged jet. The mechanism of axisymmetric instabilities is probed using an energy analysis. Axisymmetric instabilities observed during electrospinning experiments have been captured using high-speed photography. The characteristics of these instabilities (growth rate, critical wavenumber) are extracted using image analysis, and the results are compared with the predictions from the theoretical model.