The　inflation　of　circular　membranes　is　a　benchmark　problem　in　finite　elasticity.　Due　to　its　mathematical　complexity,　so　far　most　efforts　have　been　focused　on　numerical　solutions　whereas　analytical　solutions　are　still　lacking.　The　present　work　proposes　an　analytical　formula　to　compute　the　pressure–deflection　curves　of　pre-stretched　circular　membranes.　The　Mooney–Rivlin　hyperelastic　model　is　assumed　as　constitutive　law.　Following　the　semi-inverse　method,　an　analytical　model　assuming　spherical　deformed　configurations　is　developed　and　a　pressure–deflection　relation　is　derived.　Due　to　the　simplifying　hypothesis　on　the　kinematics,　the　analytical　expression　for　the　pressure　is　not　always　accurate　and　requires　an　adjustment.　Two　corrective　polynomial　functions　are　implemented　in　the　formula　to　capture　the　effect　of　the　pre-stretch,　which　affects　the　pressure–deflection　response　depending　on　the　magnitude　of　deformation　and　material　parameters.　The　polynomial　coefficients　are　calibrated　by　fitting　numerical　solutions　of　the　differential　equilibrium　equations　of　the　exact　theory.　The　calibration　is　performed　over　a　wide　range　of　material　parameters　and　pre-stretch,　covering　all　the　values　of　practical　interest.　As　a　result,　an　accurate　and　ready-to-use　pressure–deflection　relation　for　practical　applications　is　obtained.　The　proposed　formula　is　validated　by　finite　element　simulations.　Differently　from　other　solutions　in　literature,　our　formula　holds　for　both　compressible　and　incompressible　materials.　Experimental　bulge　tests　on　pre-stretched　rubber　membranes　are　carried　out　and　the　proposed　formula　is　used　for　the　calibration　of　material　parameters.　A　code　developed　in　the　software　Mathematica　is　made　available　upon　request　to　directly　compute　the　proposed　formula.　©　2022　Elsevier　Masson　SAS