This　paper　analytically　and　experimentally　investigates　the　random　vibration　problem　of　pretensioned　rectangular　membrane　structures　under　heavy　rainfall.　An　analytical　model　is　firstly　proposed.　In　this　model,　the　heavy　rainfall　is　modeled　as　a　series　of　discretized　pulse　load　whose　amplitude　follows　the　non-Gaussian　distribution;　then,　the　nonlinear　governing　equation　and　corresponding　Fokker　Planck　Kolmogorov　(FPK)　equation　of　membrane　structures　are　derived　and　solved　by　the　perturbation　method,　considering　both　the　geometrical　nonlinearity　of　structure　and　the　non-Gaussian　type　of　load;　consequently,　the　analytical　solutions　of　the　probability　density　function　(PDF),　mean　and　standard　deviation　of　displacement　response　can　be　obtained.　An　artificial　heavy　rainfall　experimental　system　is　then　developed.　This　system　is　used　to　(i)　verify　the　analytical　model　and　(ii)　evaluate　the　effects　of　rainfall　intensity,　pretension　level,　and　material　properties.　The　results　show　that　the　displacement　follows　the　significant　non-Gaussian　distribution　and　proves　strong　nonlinear　characteristics　with　increasing　rainfall　intensity　and　pretension.　The　proposed　analytical　model　can　guide　engineers　to　design　membrane　structures　from　the　perspective　of　probability.　©　2021