The costs of inbreeding depression, as well as the opportunity costs of inbreeding avoidance, determine whether and which mechanisms of inbreeding avoidance evolve. In African elephants, sex-biased dispersal does not lead to the complete separation of male and female relatives, and so individuals may experience selection to recognize kin and avoid inbreeding. However, because estrous females are rare and male-male competition for mates is intense, the opportunity costs of inbreeding avoidance may be high, particularly for males. Here we combine 28 years of behavioural and demographic data on wild elephants with genotypes from 545 adult females, adult males, and calves in Amboseli National Park, Kenya, to test the hypothesis that elephants engage in sexual behaviour and reproduction with relatives less often than expected by chance. We found support for this hypothesis: males engaged in proportionally fewer sexual behaviours and sired proportionally fewer offspring with females that were natal family members or close genetic relatives (both maternal and paternal) than they did with nonkin. We discuss the relevance of these results for understanding the evolution of inbreeding avoidance and for elephant conservation.