Translational friction and viscosity of dilute solutions of sodium poly(styrene-4-sulfonate) with molecular masses of M = (5 × 10^4)–(85 × 10^4) are studied at different concentrations of low-molecular mass salts. Molecular masses of the polymer are determined from the sedimentation-diffusion data. The study of the correlation between molecular masses and hydrodynamic characteristics resulted in ascertainment of the Kuhn–Mark–Houwink–Sakurada relationships for salt-free aqueous solutions of the polymer and solutions of the polymer in 0.2 M NaCl, 4.17 M NaCl, and 1.0 M KCl. It is shown that, as the ionic strengths of solutions are varied from minimum (H2O) to maximum (4.17 M), macromolecules of the strong polyelectrolyte sodium poly(styrene-4-sulfonate) change their conformations from rigid rods to coils and, then, approach a globular conformation. In terms of the Gray–Bloomfield–Hearst and Yamakawa–Fujii theories and within the framework of the weakly bent cylinder model, the statistical Kuhn segment length a