Porous polymer membranes are typically polymeric materials that consist of many pores and complex network structures. As a result of these features, the membranes sometimes undergo anisotropic elastoplastic deformation. Hence, it is important to investigate the deformation behavior of these materials, including anisotropic deformation under multiaxial loading. In this study, we developed a new biaxial tensile testing machine for porous polymer membranes to evaluate their deformation behavior under biaxial tension and to understand the deformation mechanisms from their microstructure. First, uniaxial tensile tests were conducted to investigate changes in Young's modulus and yield strength for different tensile directions. These tests showed that the materials underwent anisotropic deformations. Next, we developed a novel biaxial tensile testing protocol for the membranes. It is usually difficult to grip the specimens and apply uniform deformations, as the membranes have low deformation rigidity and are very thin. Thus, a gripping component was developed to enable uniform tensile deformations to be applied. Stress–strain curves for each loading axis were obtained by changing the applied strain ratio. A yield surface based on the results was created to investigate the deformation behavior under biaxial tensile loading. We also investigated the deformation mechanisms of the porous microstructure via SEM observation.