We propose a modelling approach for compressible and incompressible hyperelastic wrinkled membranes, which is compatible with general three-dimensional constitutive models. For incompressible materials, the plane stress condition is strictly enforced through an analytical approach, while for compressible materials, it is satisfied iteratively. Furthermore, the proposed hyperelastic wrinkling model is formulated within the framework of principal stretch [1] and spectral decomposition [2]. A key advantage of this approach is that the formulation relies solely on the second principal stress and its first derivative with respect to the principal stretch, leading to a more compact model representation and enhancing the efficiency of the numerical solution process. To validate the robustness and versatility of the proposed model, we conducted extensive numerical and experimental benchmark tests. The results demonstrate its great predictive capability and its suitability for implementation in both standard finite element and isogeometric analysis frameworks. This novel approach provides a reliable and efficient tool for advanced membrane wrinkling analysis, contributing to a deeper understanding of the mechanical behavior of hyperelastic membrane structures. REFERENCES [1] H. Verhelst, M., et al. Stretch-based hyperelastic material formulations for isogeometric Kirchhoff–Love shells with application to wrinkling. Computer-Aided Design 139 (2021): 103075. [2] D. Zhang, J. Kiendl, A variationally consistent membrane wrinkling model based on spectral decomposition of the strain tensor, Computer Methods in Applied Mechanics and Engineering 432 (2024) 117386.