•Relation between drag reduction and viscoelasticity of polymers is investigated.•Drag reduction correlates with extensional viscosity and Weissenberg number.•Drag reduction does not correlated with small-amplitude oscillatory shear.•For large degradation, extensional viscosity increases with decreasing strain rate. The relation between the drag reduction (DR) performance of several water-soluble polymers and their viscoelastic properties was investigated. Polymers with a flexible molecular structure including three grades of polyacrylamides (PAM), and a polyethylene oxide (PEO) were investigated. Xanthan gum (XG) and carboxymethyl cellulose (CMC), each with a rigid molecular structure, were also considered. The rheology was characterized using steady shear-viscosity measurement, capillary break-up extensional rheometer (CaBER), and small-amplitude oscillatory shear measurement at the concentration of the drag-reduced solution. To isolate the effect of shear viscosity, the concentration of the polymers was adjusted to produce solutions with a similar shear viscosity at high shear rates. Using pressure drop measurements in a turbulent pipe flow, the DR of each polymer solution was determined. With identical high-shear-rate viscosities, the flexible PAM solutions resulted in an initial DR of 50–58%, while the initial DR of PEO was 44%, and the rigid polymers provided the least DR of 12%. The rigid polymers demonstrated negligible degradation of DR over a period of 2 h. Of the flexible polymers, PAM showed moderate degradation, while the DR of PEO quickly diminished after 20 min. Drag reduction correlated with extensional viscosity and Weissenberg number obtained from CaBER. A strong correlation was not observed between DR and the viscoelastic moduli obtained from small-amplitude oscillatory shear. The large mechanical degradation of PEO was associated with a continuous extensional thickening, in which extensional viscosity increased with decreasing strain rate until the filament broke up.