Grazing lawns are recognized as important components of many savanna ecosystems, but there is no clarity on their origin or their stability in space and time. Some researchers believe soil nutrients control grazing lawn distributions. Others believe feedbacks created by herding mammals grazing in patches can promote the spread of grazing lawns without soil nutrient differences. This in turn is affected by rainfall and fire. We presented a simulation model that tests the conditions required for the initiation and spread of grazing lawns. Lawns were shown to develop in a homogeneous soil substrate, but only during periods of low rainfall, high grazer densities, and infrequent fires. Including heterogeneity in the model did not increase grazing lawn area but did reduce the effectiveness of frequent fires in preventing their establishment. We compared these results with conditions in a typical savanna park in Southern Africa. Running the model under current fire, grazing, and rainfall conditions reproduced the current grazing lawn proportions in the park. Using lower fire frequencies and higher grazer densities—such as were experienced in the park in the last 100 years—could more than double the proportion of grazing lawns in the park.