The　effect　of　vehicle　braking　can　significantly　amplify　a　bridge　deflection　compared　to　that　induced　by　a　vehicle　moving　at　a　constant　speed.　However,　the　magnitude　of　this　amplification　depends　on　vehicle　bridge　interaction　(VBI)　phenomena　activated　by　the　road　roughness.　The　road　roughness　triggers　the　vehicle　dynamics,　thus　magnifying　the　interaction　between　the　vehicle　and　the　bridge.　This　paper　proposes　a　probabilistic　model　for　the　amplification　factor.　The　amplification　factor　is　associated　with　the　vehicle’s　hard　braking　by　the　mid-span　of　the　bridge　under　different　road　roughness　classes.　The　amplification　factor,　defined　as　the　ratio　between　the　maximum　deflections　corresponding　to　a　vehicle　braking　and　moving　at　a　constant　speed,　is　estimated　as　a　function　of　the　mass,　velocity,　natural　frequency　and　damping　of　the　vehicle.　The　VBI　model　is　obtained　by　discretizing　the　coupled　governing　equations　using　the　finite　difference　method.　The　vehicle　is　modelled　as　a　two-degrees　of　freedom　system　corresponding　to　the　bouncing　and　pitching　motions.　The　computational　efficiency　of　this　model　supported　an　expensive　set　of　analyses,　where　the　parameter　values　were　selected　using　the　Latin　Hypercube　sampling　scheme.　The　model　outputs　have　been　validated　against　a　middle-span　bridge’s　measured　experimental　displacement　response　under　different　scenarios.　©　2023,　The　Author(s),　under　exclusive　license　to　Springer　Nature　Switzerland　AG.