There is a concern that high densities of elephants in southern Africa could lead to the overall reduction of other forms of biodiversity. We present a grid-based model of elephant–savanna dynamics, which differs from previous elephant–vegetation models by accounting for woody plant demographics, tree–grass interactions, stochastic environmental variables (fire and rainfall), and spatial contagion of fire and tree recruitment. The model projects changes in height structure and spatial pattern of trees over periods of centuries. The vegetation component of the model produces long-term tree–grass coexistence, and the emergent fire frequencies match those reported for southern African savannas. Including elephants in the savanna model had the expected effect of reducing woody plant cover, mainly via increased adult tree mortality, although at an elephant density of 1.0 elephant/km² , woody plants still persisted for over a century. We tested three different scenarios in addition to our default assumptions. (1) Reducing mortality of adult trees after elephant use, mimicking a more browsing-tolerant tree species, mitigated the detrimental effect of elephants on the woody population. (2) Coupling germination success (increased seedling recruitment) to elephant browsing further increased tree persistence, and (3) a faster growing woody component allowed some woody plant persistence for at least a century at a density of 3 elephants/km2 . Quantitative models of the kind presented here provide a valuable tool for exploring the consequences of management decisions involving the manipulation of elephant population densities. Keywords: African savanna, herbivory, Loxodonta africana, plant demography, spatial model, tree-grass coexistence, woody plants.