Between 2013 and 2015, over one million migrants entered Europe. Many European countries were unprepared for and overwhelmed by the rapidly unfolding, chaotic situation. To better handle future migration waves, and allow quicker exploration of government policy effects and interactions, a geospatial-based system dynamics model of migration flows across Europe was developed together with the national police of a major EU country. The model, built around subscripted data and vector operations, distributes migration inflows across the continent based on dynamic mechanisms such as societal stress, social group pull and country attractiveness. It is lightweight yet versatile, and is useful for exploratory, early-stage policy modelling, especially when investigating the system-wide effects and interactions of national migration policies.