Long‐distance dispersal is a key factor explaining the success of invasive alien species, particularly across oceanic islands. However, it is often not feasible to reliably measure long‐distance seed dispersal (LDD) over many kilometers in the field. Here, we used a three‐dimensional kinematic trajectory model (Computing Atmospheric Trajectory tool [CAT]) initiated on the basis of regional wind field data to assess the potential for LDD of a wind‐dispersed invasive tree, Spathodea campanulata (African tulip tree), across the Society Islands (French Polynesia, South Pacific Ocean) following its initial planting and spread on the island of Tahiti. The main objective of our study was to determine whether S. campanulata could be expected to spread naturally among islands. Atmospheric dynamics, seed terminal velocity, precipitation, and temperature of air masses were considered to assess the potential for LDD between oceanic islands, with the island of Tahiti serving as the island source for multiple, geographically distant invasions. Aerial trajectories of modeled S. campanulata seeds indicated that wind‐dispersed seeds originating from trees on the island of Tahiti could reach most of the Society Islands and disperse as far as 1364 km. This result suggests that Spathodea can be expected to spread naturally among the Society Islands. When rainfall events were modeled as causal agents of seed settlement, fewer seeds reached distant islands, but more seeds settled on the closest island (20 km away). Including effects of island topography (“barrier effects”) also resulted in more seeds settling on the closest island and fewer seeds reaching the most distant islands. Overall, our findings suggest that recent atmospheric models can provide valuable insights into LDD and invasion patterns of wind‐dispersed invasive species.