Long-term behavior of polymer membranes in the nonlinear regime is probed by strain histories under various stress levels. Current characterization methods for polymer membranes impose a uniform stress field and hence require a series of long-duration tests to be conducted, which poses a significant experimental challenge. Here, we present the inflated cone method to generate a continuous spectrum of strain histories under various stresses in a single experiment. By imposing a known stress gradient and utilizing a full-field strain measurement technique, the inflated cone method provides a high-throughput approach for extracting time-dependent data of polymer membranes. The method is suitable for studying nonlinear time-dependent deformations under a biaxial stress state. The stress range and ratio can be easily modulated by cone geometry design. We demonstrate the utility of the method through creep-recovery tests carried out on a polyethylene thin film. The proposed experimental method is highly beneficial for the development of nonlinear viscoelastic and viscoplastic models.