A wide range of theories and methods inspired from evolutionary biology have recently been used to investigate temporal changes in the frequency of archaeological material. Here we follow this research agenda and present a novel approach based on Approximate Bayesian Computation (ABC), which enables the evaluation of multiple competing evolutionary models formulated as computer simulations. This approach offers the opportunity to: 1) flexibly integrate archaeological biases derived from sampling and time averaging; 2) estimate model parameters in a probabilistic fashion, taking into account both prior knowledge and empirical data; and 3) shift from an hypothesis-testing to a model selection approach. We applied ABC to a chronologically fine-grained Western European Neolithic armature assemblage, comparing three possible candidate models of evolutionary change: 1) unbiased transmission; 2) conformist bias; and 3) anti-conformist bias. Results showed that unbiased and anti-conformist transmission models provide equally good explanatory models for the observed data, suggesting high levels of equifinality. We also examined whether the appearance of the Bell Beaker culture was correlated with marked changes in the frequency of different armature types. Comparisons between the empirical data and expectations generated from the simulation model did not show any evidence in support of this hypothesis and instead indicated lower than expected dissimilarity between assemblages dated before and after the emergence of the Bell Beaker culture.