A recently developed rheological technique known as continuous lubricated squeezing flow (CLSF) is adapted to perform constant stress, or creep, experiments in equibiaxial elongation flows of polymer melts. By modifying the CLSF technique, which was developed for constant strain rate deformations, we demonstrate that the technique can also be used to generate constant stress flows. Measured steady state viscosities are compared to constant rate elongation results for polymer melts having different molecular characteristics. Linear polymers show strain softening and compare well in constant stress and constant strain rate deformations. The branched polymer shows strain hardening and a viscosity that is slightly higher in constant stress for low rates. Limitations of the current version of the CLSF technique for creep flows are also briefly discussed.