The dynamics of a straight section of a jet arising during the electrospinning of a polymer solution without entanglements, and the orientation of polymer chains in the jet were explored based on the analysis of the forces balance equation and the rheological equation of the finitely extensible nonlinear elastic model. Two modes of the jet behavior were predicted. At relatively low volumetric flow rates, the straight jet has a limited length, after that, its rectilinear motion becomes impossible, while at higher flow rates, the jet always remains straightforward. It is shown that polymer chains in a jet can be strongly stretched, which leads to phase separation in a spinning solution. Aggregation of the stretched chains was also studied and the parameters of the emerging inhomogeneous structure were predicted.