Summary1. Invasive ungulates with eruptive population dynamics can degrade sensitive habitats, harbour disease-causing pathogens and facilitate the spread of weedy plants. Hence there is a need globally for cost-effective density reduction and damage mitigation strategies. User-friendly software tools that facilitate effective decision making by managers (who are not usually scientists) can help in understanding uncertainty and maximising benefits to native biodiversity within a constrained budget. 2. We designed an easy-to-use spreadsheet model -the Spatio-Temporal Animal Reduction (STAR) model -for strategic management of large feral ungulates (pigs, swamp buffalo and horses) within the World Heritage Kakadu National Park in Australia. The main goals of the model are to help park managers understand the landscape and population dynamics that influence the number and distribution of feral ungulates in time and space. 3. The model is a practical tool and methodological advance that provides a forecast of the effects and financial costs of proposed management plans. Feral animal management in the park is complex because populations cover an extensive area comprised of diverse and difficult-to-access habitats. There are also large reservoir populations in the regions surrounding the park, and these can provide immigrants even after within-park control operations. To provide the optimal outcomes for the reduction of feral animals, STAR is spatially explicit in relation to habitat, elevation and regions of culling, and applies density-feedback models in a lattice framework (multi-layer grid) to determine the optimal cost-benefit ratio of control choices. A series of spatial and nonspatial optimisation routines yielding the best cost-benefit approaches to culling are provided. 4. The spreadsheet module is flexible and adaptable to other regions and species, and is made available for testing and modifying. Users can operate STAR without having prior expert knowledge of animal management theory and application. The intuitive spreadsheet format could render it effective as a teaching or training tool for undergraduate students and landscape managers who might not have detailed ecological backgrounds.