Traffic accidents with ungulates pose a serious problem in many countries, and there is a need for predicting accidents and costs at a large scale for an efficient management of the accidents. Based on the assumption that traffic accidents are determined by traffic volume and ungulate population sizes, this study provides a relatively simple method for calculating and predicting costs of current and future traffic accidents with roe deer, wild boar, and moose in Sweden. A logistic population model is assumed for all ungulates, and econometric methods are used for predicting vehicle accidents with panel data on traffic accidents, traffic load, bags, hunting licenses, and landscape characteristics for each county and year during 2003-2015. The calculated total discounted cost of traffic accidents over a period of 15 years is relatively stable around 1300 million SEK per year in present value (which corresponds to 0.03% of gross domestic product in 2015), but the allocation of costs among ungulates differs. Costs of vehicle accidents with moose account for the largest share of the cost (44%), but accidents with wild boar show the most rapid increase over a 15 year period because of the estimated relatively high intrinsic growth rate and the recent establishment of this animal in several counties. The predicted costs are, however, sensitive to the assumption of future hunting pressure and traffic volume.