We present a method of characterizing the nonlinear stress–strain behavior of thin films of extremely soft, water-based polymer gels using uniaxial tension testing of bilayer laminates, in conjunction with methods of membrane nonlinear elasticity. A custom tensile testing apparatus is used to conduct quasi-static, uniaxial extension tests of narrow strips of thin, laminated sheets of bonded hydrogel and silicone rubber, submerged in a saline bath. The tensile load is measured via sensitive load cell and the position of material markers, at a central test-section of the sample, is optically tracked via digital image tracking methods. Stress–strain relationships are calculated for the hydrogel component of the bilayer, considered hyperelastic, homogeneous, isotropic, and incompressible, using membrane theories of finite hyperelasticity. We present the stress response for strains up to about 35% for poly(ethylene glycol) (PEG)-based hydrogels (>90% water) with polymer concentrations by weight of 5% to 10%. Polynomial functions are fit to the data for each formulation, whereby the one-dimensional strain-energy function for each formulation is determined by taking the indefinite integral.