Roof　stability　is　a　main　concern　in　tunneling　engineering.　A　modified　Mohr–Coulomb　(MC)　strength　criterion　to　reduce　the　overestimation　of　the　tensile　strength　described　from　the　MC　strength　criterion　is　employed　in　this　work.　An　analytical　stability　analysis　of　three-dimensional　(3D)　tunnel　roofs　for　both　circular　and　rectangular　tunnels　in　soil　is　performed　based　on　collapse　mechanisms　composed　of　a　series　of　right　elliptical　cones　by　limit　analysis.　Two　kinds　of　tunnel　roof　stability　measures,　that　is　the　stability　number,　and　the　minimum　supporting　pressure　required　to　ensure　the　tunnel　roof　stability　are　derived.　Optimization　codes　are　programmed　to　search　for　the　most　critical　stability　measure　solutions.　Comparative　analyses　are　conducted　to　verify　this　work,　and　the　influences　of　the　soil　strength　characteristics,　tensile　strength　cutoff,　and　the　3D　characteristics　on　both　the　stability　and　the　failure　pattern　of　tunnel　roof　are　revealed.　It　is　shown　that　a　stability　analysis　of　tunnel　roof　considering　tensile　strength　cutoff　derives　more　critical　stability　estimations,　especially　for　a　tunnel　roof　under　a　lower　internal　friction　angle　but　a　greater　cohesion.　The　3D　geometrical　characteristics　of　tunnel　roof　has　significant　influences　on　both　the　stability　measures　and　the　function　of　soil　strength　cutoff　on　the　stability　measures.　Compared　with　circular　tunnels,　supporting　pressures　will　always　being　needed　for　rectangular　tunnels　to　maintain　the　stability　of　tunnel　roof,　especially　under　a　full　tensile　strength　cutoff　condition.　©　The　Author(s),　under　exclusive　licence　to　Springer-Verlag　GmbH　Germany,　part　of　Springer　Nature　2024.