A thin sheet (membrane) of the polymeric material is clamped between a Teflon-coated thermostated plate and a thermostated aluminium cylinder. By applying thermostated air through the plate, the polymer membrane deforms into an elliptic or a circular cylinder. The position of the top of the inflating membrane is detected by fibreoptic sensors positioned in the cylinder. The pressure difference across the inflating membrane is measured as well. Measurements were performed on a polyisobutylene melt. As the deformation in this device is highly non-uniform, the response of the material is modelled by a finite element method (the 3D Lagrangian integral method). Here, the non-linear properties are modelled with a constitutive equation of the Factorised K-BKZ type, using a potential function F((ln u')), where (In u') represents the potential function from the Doi-Edwards reptation theory. The Linear viscoelastic properties of the material (the time dependence) have been obtained from oscillatory shear measurements and modelled with a continuous relaxation spectrum (BSW) as a memory function, using a leastsquare method. This allows the strain dependence in the constitutive equation to be estimated, based on numerical simulations and experimental measurements of the membrane inflation.