The present study examines the stability of a thinning straight jet in electrospinning process. The linear stability analysis is carried out to obtain the growth/decay rate of axisymmetric disturbance imposed on the thinning jet. The analysis captures the role of solvent evaporation in the stability behavior of the linear path of the electrospinning jet. In contrast to many prior stability analyses which consider the jet as a cylindrical filament with uniform radius, the present study analyzes the stability of a jet which exhibits thinning under realistic electrospinning conditions. Two different polymeric solutions are considered: the poly-isobutene (PIB) Boger fluid with low electrical conductivity and the highly conductive poly-ethylene oxide (PEO) solution in ethanol/water. At low extensional deformation, the rheology of the unentangled PIB-based Boger fluid is described by the Oldroyd-B model. The PEO solution, on the other hand, experiences a very high elongation rate due to the development of strong axial electric stress. The nonlinear rheology of the entangled PEO solution is appropriately described by the eXtended Pom–Pom (XPP) model, a variant of the classical tube model. The analysis reveals that the instability in low conductivity fluid is driven by the capillary forces, whereas the high conductivity fluid exhibits oscillatory conducting mode of instability driven by the coupled effect of axial electric field and surface charges. For both the reference fluids, the increase in solvent evaporation tends to decrease the disturbance growth rate to the extent that the axisymmetric instability is completely suppressed for a strong enough evaporation. The stabilizing role of solvent evaporation is attributed to the enhancement in fluid viscosity and elasticity due to increased polymer concentration upon evaporation. Thus, by suppressing the onset of axisymmetric instability during the straight jet path, solvent evaporation potentially helps produce smooth fibers without bead formation. © 2020 Elsevier Ltd