A novel experimental technique to study the rheological behavior of polymer melts and other viscous fluids in equibiaxial elongational deformations is described. The new technique is a modification of lubricated squeezing flow (LSF) wherein deformation is induced by compression of the sample between parallel plates having a thin film of a low-viscosity fluid or lubricant. In previous work, we have demonstrated that despite its simplicity, LSF is limited to rather small strains because of uncontrolled lubricant film thinning. The new technique, which we call continuous lubricated squeezing flow (CLSF), resolves the lubricant thinning problem by replenishing the lubricant films with a continuous and uniform flow of lubricant through porous plates. The CLSF technique is validated in constant strain-rate deformations by direct comparison with published data obtained using a considerably more complicated device developed by Meissner and co-workers [Hachmann, P., and J. Meissner, "Rheometer for equibiaxial and planar elongations of polymer melts," J. Rheol. 47, 989-1010 (2003)]. (c) 2010 The Society of Rheology. [DOI: 10.1122/1.3474599]