A linear stability analysis is carried out for viscoelastic filaments (formed by an unentangled polymer solution) during capillary thinning in the regime of unfolded polymer coils taking into account the relative motion of the solvent and the polymer. The conditions for the onset of filament instability with respect to axisymmetric modulation of its surface are found. The analysis is valid for relatively fast processes occurring at times shorter than the characteristic thinning time. It is shown that the growth rate of such pearling instability is determined by the osmotic modulus of the solution and the degree of orientation of macromolecules. In the case of nonassociative polymers, the instability develops (with the growth rate exceeding the rate of filament thinning) when the longitudinal length of stretched polymer chains exceeds the diameter of the filament. The theory is also applicable to soft gels and associative polymer solutions with very long relaxation times. The predictions of the theory are in agreement with experimental data.

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