Despite its technological significance, the rheological behavior of polymer melts in equibiaxial elongational flow is largely unexplored and, consequently, is inadequately understood. The simple reason for this is that methods for generating equibiaxial elongational deformations are either very complicated or not reliable. The most widely accepted method for generating rheologically controlled, equibiaxial elongational flow is the rotating clamp method, or MultiAxiale Dehnung (MAD), developed by Meissner. However, the extremely complicated nature of the MAD rheometer has resulted in a relatively limited set of experimental data. A promising method that has been used with some success is known as Lubricated Squeezing Flow (LSF), where a polymer melt is squeezed between lubricated surfaces. Unfortunately, uncontrolled lubricant thinning limits the LSF technique to rather modest strain levels. Here we report the first direct comparisons of data obtained with the LSF and MAD techniques. These comparisons were made using the same polystyrene and low-density polyethylene melts used by Meissner. We find that the data obtained using LSF deviate from the MAD data at Hencky strains of less than one, and display behavior that could easily be mistaken for strain hardening. The main objective of this study is the development of a modified LSF technique that involves the continuous injection of lubricant through porous metal plates. Design and fabrication issue of the modified technique are briefly discussed. We also report the first measurements of transient equibiaxial elongational viscosity obtained using the modified LSF technique and make comparisons with data from the MAD rheometer.