In the recent decades, electrospinning was mainly concerned with the formation of nanofibers from synthetic polymers and natural polymers targeting predominantly technical applications areas such as textiles and filters. In this paper, the effect of nonlinear matter flow on the dynamics of electrified jets in electrospinning process is examined by analyzing the bead-spring model. The ordinary differential equation is derived from momentum equation which is solved numerically using the fourth-order Runge-Kutta method. The simulations show good agreement with the experimental data and provide a qualitative understanding of the role of viscoelasticity in the early stage of the electrospinning experiment. The results show that a non-Newtonian rheology can slow down the elongation dynamics, thereby reducing the stable jet length.