A model of handedness incorporating both genetic and cultural processes is proposed, based on an evolutionary analysis, and maximum-likelihood estimates of its parameters are generated. This model has the characteristics that (i) no genetic variation underlies variation in handedness, and (ii) variation in handedness among humans is the result of a combination of cultural and developmental factors, but (iii) a genetic influence remains since handedness is a facultative trait. The model fits the data from 17 studies of handedness in families and 14 studies of handedness in monozygotic and dizygotic twins. This model has the additional advantages that it can explain why monozygotic and dizygotic twins and siblings have similar concordance rates, and no hypothetical selection regimes are required to explain the persistence of left handedness.