Interference can be defined as the reduction of intake rate caused by the presence of congeneric individuals. However, surrounding congeneric individuals may also accelerate food depletion. Therefore, it is difficult to quantify interference (contest) and exploitative (scramble) competition separately, particularly in the field. In an individual-based model, where food was immediately replenished in patches after a foraging bout, we isolated the effect of interference competition. In this way, we investigated how interference shapes the intake rates of flocking Bewick’s swans, Cygnus bewickii, consuming tubers of fennel pondweed, Potamogeton pectinatus. The model predicted that intake rate declines with increasing swan density, and that the rate of decline is greater in subordinate birds than in dominant birds. Subordinate birds suffered a large reduction in intake rate at high densities because they spent a large proportion of the time avoiding more dominant individuals. A major decline in intake rate of subordinates occurred close to the maximum swan densities observed in the field. We expected subordinates to leave high-density flocks and look for another foraging location: interference competition seemed to regulate the maximum swan flock density in the field. Hence, the mean population intake rate at realized densities was only slightly lower than in the absence of interference. As interference occurred mainly as avoidance behaviour, which is difficult to observe in the field, it might commonly remain cryptic for the observer. Our results may explain other field studies where interference competition seemed to be of lesser importance.