Abstract.Assemblages of corals characterise specific reef biozones and the environmental conditions that change laterally across a reef and with depth. Drill cores through fossil reefs record the time-and depth-distribution of assemblages, which captures a partial history of the vertical growth response of reefs to changing palaeoenvironmental conditions. The effects of environmental factors on reef growth are well understood on ecological time-scales but are poorly constrained at centennial to millennial 5 timescales. pyReef-Core is a stratigraphic forward model designed to solve the inverse problem of unobservable environmental processes controlling vertical reef development by simulating the physical, biological and sedimentological processes that determine vertical assemblage changes in drill cores. It models the stratigraphic development of coral reefs at centennial to millennial timescales under environmental forcing conditions including accommodation (relative sea level upward growth), oceanic variability (flow speed, nutrients, pH and temperature), sediment input and tectonics. It also simulates competitive 10 coral assemblage interactions using the generalised Lotka-Volterra system of equations (GLVEs) and can be used to infer the influence of environmental conditions on the zonation and vertical accretion and stratigraphic succession of coral assemblages over decadal timescales and greater. The tool can quantitatively test carbonate platform development under the influence of ecological and environmental processes, and efficiently interpret vertical growth and karstification patterns observed in drill cores. We provide two realistic case studies illustrating the basic capabilities of the model and use it to reconstruct (1) the 15 Holocene history (from 8,500 years to present) of coral community responses to environmental changes, and (2) the evolution of an idealised coral-reef core since the Last Interglacial (from 140,000 years to present) under the influence of sea-level change, subsidence and karstification. We find that the model reproduces the details of the formation of existing coral-reef stratigraphic sequences both in terms of assemblages succession, accretion rates and depositional thicknesses. It can be applied to estimate the impact of changing environmental conditions on growth rates and patterns under many different settings and 1Geosci. Model Dev. Discuss., https://doi