In the ability and motivation to copy others, social learning has been shown to provide a mechanism for the inheritance of behavioural traditions. Major questions remain about the circumstances and models that shape such social learning. Here, we demonstrate that behavioural food-processing variants among wild vervet monkey, Chlorocebus aethiops, mothers are matched by their infants in their first manipulative approaches to a new foraging problem. In our field experiment, grapes covered with sand were provisioned within groups of wild vervet monkeys that included experienced adults and 17 nave infants. Monkeys dealt with the dirty food in four different ways. All infants first adopted their mother's way of handling the grapes, rather than those of other mothers or other monkeys eating nearby. Mothers who handled grapes in different ways had infants who were more likely to explore different approaches to handle the sandy grapes. Rarer cases of co-feeding siblings further suggest that copying may occur on the matriline level. Our findings suggest a capacity for detailed copying by infants of their mothers' and matriline members' food-processing techniques when encountering new foods, underlining the significance of familial models in such primate social groups.