In　the　present　work　we　derive　an　analytical　expression　for　the　pressure–deflection　curve　of　circular　membranes　subjected　to　inflation.　This　problem　has　been　studied　mostly　from　a　numerical　point　of　view　and　there　is　still　a　lack　of　accurate　closed-form　solutions　in　nonlinear　elasticity.　The　analytical　formulation　is　developed　with　a　semi-inverse　method　by　setting　a　priori　the　kinematics　of　deformation　of　the　membrane.　A　compressible　Mooney–Rivlin　material　model　is　considered　and　a　pressure–deflection　relation　is　derived　from　the　equilibrium.　The　kinematics　is　approximated　and　therefore　the　obtained　solution　is　not　exact.　Consequently,　the　formulation　is　adjusted　by　introducing　an　additional　polynomial　function　in　the　pressure–deflection　equation.　The　polynomial　is　calibrated　by　fitting　numerical　solutions　of　the　exact　system　of　differential　equilibrium　equations.　The　calibration　is　done　over　a　wide　range　of　constitutive　parameters　that　covers　the　response　of　all　rubber　materials　for　technological　applications.　As　a　result,　a　definitive　and　accurate　expression　of　the　applied　pressure　as　a　function　of　the　deflection　of　the　membrane　is　obtained.　The　formula　is　validated　with　finite　element　(FE)　simulations　and　compared　with　other　solutions　available　in　the　literature.　The　comparison　shows　that　the　present　model　is　more　accurate.　In　addition,　unlike　the　other　models,　it　can　be　applied　to　compressible　materials.　Experimental　uniaxial　and　bulge　tests　are　carried　out　on　rubber　materials　and　the　model　proposed　is　used　to　characterize　the　Mooney–Rivlin　constitutive　parameters.　Since　the　pressure–deflection　formula　is　accurate　and　easy-to-use,　it　is　an　innovative　tool　in　engineering　applications　of　inflated　membranes.　©　2022　Elsevier　Ltd