The equibiaxial elongational viscosity of six commercially available polymer melts is measured using a novel technique known as continuous lubricated squeezing flow. This technique is a modification of simple lubricated squeezing flow. The systems were chosen in order to investigate the dependence of equibiaxial elongational viscosity on molecular structure. Three of the melts are polyethylene with long chain branching, two are polyethylene with short chain branching, and one is polyisobutylene with linear chains. Each polymer was subjected to strain rates ranging from 0.003 to 0.1 s−1 and compared to the linear viscoelastic prediction so that the degree of strain hardening could be determined. For a modestly branched polymer, comparison of rheological behavior in both uniaxial and equibiaxial deformations was possible. POLYM. ENG. SCI., 55:1012–1017, 2015. © 2014 Society of Plastics Engineers