Electrospinning is a process in which solid fibers are produced from a polymeric fluid stream delivered through a millimeter-scale nozzle. The aim of this research is to study the effects of prominent parameters in terms of non-dimensional numbers on the process with and without centrifugal force. For this purpose, a numerical model is developed to solve governing equations and the obtained results are validated with the existing numerical and experimental results. In this model, the hydrodynamics equations are simplified by a perturbation method and the boundary integral method is used to solve the Electrostatic equations. Then by forcing the boundary conditions at the interfaces for the stresses, the two set of equations are coupled. The governing EHD equations are discretized via a second order central finite difference method and the resulting system of equation is solved by using a Newton like iterative method. In this study also, the electrical behavior of system is considered as the leaky dielectric and dielectric fluid models for the liquid jet and surrounding fluid, respectively. For the leaky dielectric model, low conductivity of the fluid causes the formation a thin layer near the interface of the electric charges. Here, we assume that the charge redistribution occurs instantly and a static model for charges is acceptable. Also, the presence of nozzle in between of two electrodes makes a non-uniform electric field in the vicinity of the nozzle and, consequently, increases the magnitude of the electric field. In some previous simulations, the nozzle geometry and its effect on the external electric field were included in the simulations. However, in this study, the nozzle effect is automatically included by applying proper boundary condition at the nozzle (R(0) = 1) in the BEM formulation. Moreover, an analytical method is used to remove the singularity at the axisymmetric boundary. Finally, the method is validated against several benchmark problems. Then the method is used to predict the reduction in the jet radius along the axis of the jet (jet elongation) and the jet center line deviation in the horizontal plane ( - ) when the dimensionless numbers such as Weber, Reynolds, Farad, Roy, Beta and aspect ratio are changed. Results shows that in electrospinning, the Weber and Beta dimensionless numbers are very effective in the jet radius reduction and comparing the present results with the other numerical and experimental results confirms that the static model for electric charges is accurate only at low volume flow rate and high applied electric field. In electro-centrifuge spinning, the jet elongation is severely affected by Roy and aspect ratio. By increasing Reynolds, Roy, Beta and aspect ratio, and reducing Weber dimensionless numbers, the deviation of jet center line from a straight line is increased. Also, at high rotational speeds the process is only controlled by the centrifugal force and other electric parameters, represented by Beta in the momentum equation, have little influence on the results. Keywords: Liquid jet, Electric, Leaky dielectric, Perturbation, Boundary integral, Centrifuge