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In this paper, we provide a theoretical investigation of axisymmetric instabilities observed during electrospinning, which lead to beads-on-a-string morphology. We used a discretized method to model the instability phenomena observed in the jet. We considered the fluid to be analogous to a bead-spring model. The motion of these beads is governed by the electrical, viscoelastic, surface tension, aerodynamic drag, and gravitational forces. The bead is perturbed at the nozzle, and the growth of the instability is observed over time, and along the length of the jet. We considered both lower electrical conducting polyisobutylene (PIB)-based Boger fluids and highly electrical conducting, polyethylene oxide (PEO)/water systems. In PIB fluids, the onset of the axisymmetric instability is predominantly based on the capillary mode, and the growth rate of the instability is decreased with the viscoelasticity of the jet. However, in the PEO/water system, the instability is electrically driven, and a significant increase in the growth rate of the instability is observed with the increase in the voltage. Our predictions from the discretized model are in good agreement with the previous linear stability analysis and experimental results. Our results also revealed the non-stationary behavior of the disturbance, where the amplitude of the perturbation is observed to be oscillating. Furthermore, we showed that the discretized model is also used to observe the non-axisymmetric behavior of the jet, which can be further used to study the bending instability in electrospinning. [ABSTRACT FROM AUTHOR]