The equations for steady isothermal spinning of a viscoelastic liquid are solved for a fluid model with constant modulus and a single constant relaxation time. High stress levels are predicted for elastic liquids, and the velocity approaches a linear profile in the limit of maximum drawdown. These predictions are in accordance with the observed behavior of polymeric liquids in isothermal spinning. Relaxation times computed from spinning data of Spearot and Metzner and Acierno et al. for four low density polyethylene melts are comparable to those measured rheogoniometrically, though the spinning relaxation times are 20 to 80% larger.