The problem of the squeezing of a fluid film with a complex rheology is studied. Thefluid is represented by the Phan-Tien and Tanner (PTT) constitutive equation. The goal ofthe paper is to develop an analytical approach which allows one to describe and quantifythis process, which is often present in classical lubrication problems, but particularlyin human joints. The present approach can potentially supplement time-consuming and costlypurely numerical methods which are also susceptible to misleading artifacts. A parametricstudy reveals the effect of fluid elasticity compared to viscous effects and someexplanation is suggested as to their possible links with joint diseases.