Modelling of long-distance travel is often overlooked in national transport models, which is problematic, for example, when assessing the impacts of large railway investments involving a substantial share of cross-border travel. One kind of long-distance travel is visitors’ trips. In this paper, we estimate trip generation, mode and destination choice models for visitors’ long-distance trips to Sweden using survey data on incoming visitors collected at the Swedish border and major airports and ferry terminals. We describe the modelling challenges faced, such as having origin data on the country level only. We explain visitor choice of the destination zone in Sweden using point-of-interest data from open-street-map. Travel time and travel cost elasticities are calculated for a railway investment scenario. The results show that reducing door-to-door travel time by rail is more important than reducing travel costs if the goal is to switch visitors’ trips from air and car to rail.