The　spatiotemporal　variability　exists　in　almost　all　engineering　problems,　since　the　environmental　actions　and　material　properties　may　change　both　spatially　and　temporally　in　a　stochastic　manner.　Therefore,　reliability　analysis　is　inherently　space–time-dependent.　In　this　study,　an　innovative　space–time-dependent　outcrossing　rate　(STOR)　method　is　proposed　for　dealing　with　such　reliability　problems.　The　failure　probability　of　a　structure　is　determined　based　on　outcrossing　rate　which　is　theoretically　derived　for　the　first　time,　considering　the　spatiotemporal　variability　of　all　basic　variables.　Then,　an　efficient　numerical　algorithm　for　computing　the　failure　probability　is　proposed　based　on　Gauss-Legendre　quadrature.　The　application　of　STOR　method　is　investigated　through　three　examples,　including　non-Gaussian　random　processes,　non-Gaussian　random　fields,　strong　nonlinear　limit　state　functions　and　small　failure　probability　problems.　The　proposed　STOR　method　is　found　to　be　efficient　for　space–time-dependent　reliability　analysis　with　enough　accuracy.　©　2023　Elsevier　Ltd