Masonry arch bridges (MABs) comprise a significant proportion of bridge stock in many countries and despite their often considerable age, they continue to perform as vital pieces of infrastructure. Increasing flood events in relation to climate change in the last two decades show that MABs are vulnerable to flood-induced loads. Although much existing work has focused on the substructure of MABs and the associated quantification of scour depth, the authors’ previous work was one of the first studies to investigate flood-bridge superstructure interaction for a single-span masonry arch bridge. The present paper quantifies the flood-induced hydrostatic, hydrodynamic and debris impact pressures and forces on a typical pier of a multi-span MAB with a triangular cutwater using a two-way coupling method between the fluid and the structure. The meshless smoothed particle hydrodynamics (SPH) and discrete element method (DEM) approaches are used to model the flood flow and the structures (bridge pier and floating debris), respectively. The SPH-based DualSPHysics software is coupled with the multi-physics library Project Chrono to achieve the two-way coupling whereby the deformation of the structure is modelled in compliance with the flow. The results indicate that the SPH-DEM method can capture the complex physics of both flood and floating debris interactions with the bridge pier and reveal significant forces can be generated.