This paper reports the results of modelling the biaxial extension of soft solids in lubricated squeezing flow geometry. The nonlinear constitutive model including the single mode Phan-Thien Tanner (PTT) model has been used to model the behaviour of different materials such as a soft tissue (pig liver) and three wheat flours with different protein contents. These were used to evaluate the usefulness of the method and to establish how different compositional or structural parameters could be relevant in determining the rheological behaviour of soft solids. From this study it was found that homogeneous uniaxial compression can be achieved in lubricated squeezing flow. Modelling results are in good agreement with experimental results for all the materials considered.