A method to characterize the bulk hydrated properties of soft polymers and hydrogels, whose moduli are in the low MPa regime, using the pressure-bulge technique is presented. The pressure-bulge technique has been used extensively in the characterization of thin films, particularly for the case of metals. The extension of the plane-strain and circular bulge techniques to determine the Young's modulus and Poisson's ratio of bulk latex and silicone rubber sheets are shown here, in addition to the viscoelastic behavior of 5% agarose gels in the time domain using relaxation tests. The membranes are clamped between two stainless steel plates that are connected to a liquid pressure chamber. A syringe connected to a linear actuator causes changes in the pressure and displacement, and a pressure sensor and confocal displacement sensor are used to monitor these changes in real time. The theory presented converts the measured pressure and displacement data into stress and stretch data, using a geometrically nonlinear analysis, and the elastic/viscoelastic properties are then determined from this data. The results from the bulge tests are compared with data from uniaxial tension tests on hydrated specimens, and the data comparison with respect to each of the materials tested show good agreement between the two measurements. These results show promise regarding the use of pressure-displacement techniques to characterize other soft material systems, including biological polymers and tissues, as well as cell-to-matrix and cell-to-cell interactions under varying mechanical loading conditions of cell substrates.