Tourism in the Arctic archipelago of Svalbard, Norway, has increased significantly in the last decade. Cruise ships make landings all around the archipelago, and there are numerous snowmobile, boat and hiking excursions. We describe disturbance effects on the three geese species that breed in Svalbard: the pink‐footed goose (Anser brachyrhynchus), the barnacle goose (Branta leucopsis) and the light‐bellied brent goose (Branta bernicla hrota). All three are regarded as highly vulnerable to disturbance. Behavioural responses by geese to humans on foot were analysed by estimating the distances at which geese become alerted, the escape flight distances and the length of escape flights, during pre‐nesting, nesting and brood‐rearing periods. We evaluate the consequences of human intrusion on the reproductive success in breeding colonies. During all three phases, pink‐footed geese responded at longer ranges, and flew/ran longer distances, than both brent and barnacle geese: when disturbed on the nest site, both male and female pink‐footed geese flew far away, resulting in a high rate of nest loss to avian predators (35%), compared with the 4 and 0% losses among barnacle and brent geese, respectively. During brood rearing, families of pink‐footed geese escaped at an average distance of 1717 m, compared with distances of 620 and 330 m for brent and barnacle geese, respectively. Even though bird sanctuaries have been established on several islets, with no human access during nesting, many core areas for the three species remain without restrictions, such as islets used by brent geese and slopes and valleys with nesting pink‐footed geese, brood‐rearing areas and moulting grounds for non‐breeding geese. We propose regulations of human access to goose concentration areas, and address the need to better protect these significant areas. We also discuss the need for further research on the vulnerability of geese to human activity.