Melt viscosity data were obtained for linear and branched ethylene polymers over temperatures of 150 to 250°C and shear rates of about one to 300 sec −1 . A capillary rheometer was employed, and the appropriate corrections were made for the several sources of significant error in shear stress and shear rate. These corrected data were analyzed in terms of the Ree‐Eyring inverse hyperbolic sine relationship for viscous flow. The molecular structure was determined by infrared absorption analyses and molecular weight determinations. The rheological character of these polyethylenes was found to depend on the weight‐average length of the polymer backbone and on the branching. The major contribution to the viscosity depended on the length of the backbone and was associated with the longer relaxation times. An additional contribution to the viscosity depended on molecular segments about equal to the interbranch distance, and was associated with the shorter relaxation times. The temperature effect was found to depend on the number of the long‐chain branches, as interpreted by the reduced variable procedure applied to the shear rate.