In the present research circular sheets of rubber or soft fetal membrane tissue are inflated within the confines of a cylindrical tube under hydrostatic pressure. The resulting deformations, which are surfaces of revolution, are described and analyzed. The experimental method of deforming the membranes was chosen so that the deformation profiles would have physiological similarity to the expansions of the chorioamniotic sac during the period of labor in the final stage of pregnancy. The kinematical response of the fetal membranes is shown to be the same as the kinematical response of rubber. The principal extension ratios are calculated for a rubber membrane for several deformation profiles. From data obtained in deflection experiments with rubber an approximate deflection profile is established. Assuming rubber to be a Mooney material, and using the theory of elastic membranes described by Green and Adkins, displacements, slopes, and second derivatives of a refined deformation profile for rubber are derived as a function of the maximum displacement at the pole. Using these results it is shown that one can evaluate the elastic parameters of human fetal membranes. In this manner one can make a meaningful comparison of the elastic nature of fetal membranes from term pregnancies to the elastic nature of membranes which rupture at various gestational stages.