This study investigated creep deformation behavior of a porous polymer membrane under biaxial stress by using the small-punch test. We first conducted a mechanical test for creep deformation, using uniaxial tension to examine creep compliance, which revealed that creep compliance was strongly dependent on applied stress in a nonlinear creep-deformation relationship. Using the time–temperature–stress superposition principle (TTSSP), we obtained a master curve that unified the compliance curves for various applied stresses. Next, a small-punch test was conducted to apply biaxial stress to the membrane. This method was also able to apply a stress gradient to the membrane during the test. Creep deformation due to the small-punch test was found to be dependent on the applied load. Additionally, we created a homogenous model based on the finite element method (FEM) and the TTSSP of nonlinear creep theory. The FEM model predicted creep deformation behavior during a small-punch test for various load levels with good accuracy.