Wind　loads　in　most　random　vibration　studies　are　assumed　to　follow　Gaussian　processes,　and　reliability-based　design　is　generally　conducted　based　on　moment　methods　to　ensure　structural　survivability.　However,　membrane　roofs　under　typhoon　attacks　are　loaded　by　strong　non-Gaussian　random　excitations.　The　contributions　of　the　third-order　moment　(skewness)　and　fourth-order　moment　(kurtosis)　to　the　structural　reliability　become　more　significant.　This　study　investigated　the　stochastic　dynamic　response　and　reliability　of　hyperbolic　parabolic　membrane　structures　excited　by　non-Gaussian　wind　loads.　Firstly,　the　Fokker-Planck-Kolmogorov　(FPK)　governing　equation　of　membrane　structures　is　established,　with　considerations　of　both　geometric　nonlinear　stiffness　and　nonlinear　motion-induced　aerodynamic　force.　Then,　the　steady-state　displacement　response　is　analyzed　in　the　slow-varying　process　of　the　system.　Consequently,　a　series　of　analytical　solutions,　including　probability　density　function　(PDF),　root　mean　square　(RMS)　value,　skewness,　and　kurtosis,　can　be　obtained.　The　accuracy　of　the　proposed　theoretical　model　is　validated　throughout　a　number　of　wind　tunnel　tests　including　various　wind　velocities　and　directions.　The　effects　of　geometric　nonlinear　stiffness　term,　nonlinear　motion-induced　aerodynamic　force,　reduced　wind　velocity　and　rise-span　ratio　on　structural　reliability　are　thoroughly　discussed.　The　findings　reveal　that　the　structural　extreme　response　shows　strong　non-Gaussian　behavior,　featured　with　skewness　of　-1.5　∼　1.2　and　kurtosis　of　3.82　∼　6.89.　The　influence　of　geometric　nonlinear　stiffness　and　nonlinear　motion-induced　aerodynamic　force　on　structural　reliability　can　reach　up　to　28.42　%　and　29.84　%,　respectively.　Among　various　design　parameters,　the　reduced　wind　velocity　shows　the　most　significant　influence　on　structural　reliability.　In　the　probability-based　design　framework,　the　critical　reduced　wind　velocity　is　identified　as　1.2,　and　the　critical　rise-span　ratio　is　recommended　as　1/10.　The　research　proposed　in　this　paper　provides　an　accurate　analytical　model　for　predicting　the　dynamic　behavior　of　such　flexible　structures　under　typhoons.　©　2024　Elsevier　Ltd