Fatigue　of　heavy-haul　railway　bridges　caused　by　large　and　frequent　cyclic　loads　has　become　a　serious　concern　to　all　stakeholders　of　the　bridges.　The　dynamics,　temporal,　and　stochastic　features　of　such　loads　make　it　very　difficult　to　assess　the　fatigue　performance　of　the　bridges.　The　aim　of　this　study　is　to　propose　a　stochastic　analysis　method　of　stress　range　for　heavy-haul　railway　bridges　that　can　capture　such　features.　First,　the　dynamic　stress　range　response　of　the　bridge　is　obtained　from　the　coupled　train-track-bridge　system.　Then,　the　stress　range　is　modeled　as　a　continuous　nonstationary　stochastic　process　based　on　its　stochastic　characteristics　throughout　the　bridge　design　life.　To　describe　its　probabilistic　characteristics,　a　moment-based　method　is　employed,　enabling　a　flexible　representation　of　its　marginal　distribution　and　autocorrelation　function.　Finally,　the　method　is　applied　to　analyze　the　stress　range　of　an　actual　railway　steel　bridge,　demonstrating　its　practical　applicability.　It　is　found　in　this　study　that　the　marginal　distribution　of　the　stress　range　can　be　approximated　as　a　cubic　normal　distribution　with　good　accuracy,　and　that　the　autocorrelation　function　indicates　the　clear　time　dependency　of　the　stress　range.　A　merit　of　the　proposed　method　is　that　it　can　capture　the　temporal　and　random　characteristics　of　dynamic　loads　on　steel　bridges.　The　contribution　of　this　study　is　the　provision　of　good　guidance　for　engineers　and　asset　managers　in　the　assessment　and　management　of　heavy-haul　railway　bridges　under　fatigue　loads.