Abstract: Flexible membrane structures are widely used in the key parts of aerospace vehicles. Surface flatness is one of the main factors affecting the performances of membrane structures. Wrinkle amplitude is an important factor for evaluating the surface flatness of membrane reflector antennas. Wrinkle amplitude is strongly related with the transverse strain, perpendicular to wrinkling direction. Based on the stability theory of thin plates, a theoretical model is proposed to predict the wrinkle amplitude in a square membrane subjected to diagonal tension. The effect of transverse tensile force on the membrane deformation is taken into account. The displacement perpendicular to wrinkling direction is decomposed into three parts: the transverse displacement induced by Poisson's effect, the wrinkling displacement induced by out-of-plane deformation, and the tensile displacement induced by transverse tensile force. The formulation of wrinkle amplitude is reworked. Based on digital image correlation (DIC) technology, speckle experiment is carried out for a square membrane subjected to diagonal tension. The three-dimensional displacement of square membrane is measured by the binocular vision three-dimensional measurement system. The three-dimensional deformed shapes and wrinkle waveforms of membrane are obtained. We study the nonlinear relationship between wrinkle amplitudes and tensile loads. Compared with an existing model, our model greatly improves the accuracy of prediction to wrinkle amplitude, which is in good agreement with experimental results. The theoretical research presented in this paper can provide valuable guidance for the establishment of a fine numerical model and the implementation of algorithm.