In many systems the use of traditional shear rheometry suffers from slip related issues which can lead to large errors in the measurement of apparent theological properties. For this reason for a long time there has been considerable interest in alternative methods for the measurement of many 'difficult' materials such as suspensions. One such alternative method is to use a squeezing flow between a pair of parallel discs. In the current work a fully coupled pair of non-linear ordinary differential equations are derived describing the evolution of the flow of a sample film sandwiched between a pair of lubricant films and a pair of plates. Here the flow fields are derived from the radially symmetric stream function solution in contrast to previously published approaches which invoke the lubrication approximation. Three clear flow regimes are identified: 'super-lubricated', apparent slip, and lubrication failure. Which of these regimes is observed in a particular experiment depends on the viscosity ratio, relative thicknesses of the films and the applied stress or strain, respectively. Finally, the possibility of pumping an additional amount of lubricant fluid through the top plate in order to ensure pure bi-axial stretching of the sample film is investigated. It seems that it is possible to achieve this, at least from a theoretical perspective, although the control of the lubricant flow through the top plate must be carefully adjusted as a function of the system evolution. (C) 2004 Elsevier B.V. All rights reserved.