To analyze the durability of electrospun fibrous membranes, the evaluation of their elastic properties becomes essential. The present work focuses on the evaluation of elastic properties of randomly- oriented nanofibrous thermoplastic polyurethane elastomer membranes via experimental technique and numerical modeling. For this purpose, the membranes are fabricated using electrospinning technique. From the Scanning Electron Microscopy analysis, it is found that the fibers are randomly-oriented with an average diameter of 606 nm. The tensile test results suggest that the membranes are isotropic in the plane with Young’s modulus and in-plane Poisson’s ratio of 1.31 MPa and 0.54 respectively. In addition to experimental evaluation, numerical modeling based on linear elastic homogenization of SEM images is employed to predict the membrane’s elastic properties. Results show that the model provides excellent estimation of membrane Young’s modulus. However, the estimation of Poisson’s ratio is slightly difficult due to the limits in the model at high deformations.