Tensile membranes have gained widespread preference in applications such as long-span stadiums, community centres, airports, and public spaces due to their economic benefits, lightweight nature, and aesthetic appeal. These membranes are also commonly utilized in mechanical and aerospace systems. However, their inherent flexibility makes them susceptible to wind-induced excitations, leading to instability in the form of flutter or divergence beyond a certain threshold wind velocity. This study presents a detailed analysis of aerodynamic instability in a planar, prestressed, orthotropic rectangular membrane. The governing differential equations of motion are derived by incorporating geometric nonlinearity through von Kármán’s large deformation theory. The aerodynamic loading on the tensile membrane is modelled utilising the thin airfoil theory in aerodynamics in conjunction with the potential flow theory in fluid mechanics. The resulting nonlinear differential equations are solved using the Bubnov-Galerkin method, by including the higher modes in the analysis. Eigenvalue analysis is performed on the linearized system of equations to assess the system’s stability. A parametric study is carried out to examine the influence of key parameters, including along-wind span, membrane pretension, and pretension ratio, on critical wind velocity. The investigation highlights the significant impact of membrane prestress and higher modes on the aerodynamic instability of the membrane structure.