To evaluate the lowest polymer concentration within a solvent from which there appears beadless nanofibres during the process of electrospinning, is rather complicated. A widely used method is based on a determination of so called entanglement concentration c(e) and the onsets of beadless nanofibres are characterized by multipliers of c(e) subjected to used materials. However, a determination of c(e) as an intersection point of two linear segments (in log-log coordinates specific viscosity vs. concentration) in a semi-dilute region is not applicable for all materials as for instance a solution of poly(ethylene oxide) (PEO) in water does not exhibit 'classical' three linear segments within the dilute and semi-dilute regions determining overlap and entanglement concentrations. For such cases a new approach for the evaluation of an initial concentration from which beadless nanofibres are produced is proposed. This method does not use the terms overlap and entanglement concentrations. The procedure is demonstrated using four PEO solutions differing in molecular weight. The relationship expressing initial concentration in dependence on PEO molecular weight containing no adjustable parameters is proposed.