Automating the learning of causal models from sample data is a key step toward incorporating machine learning in the automation of decision-making and reasoning under uncertainty. This paper presents a Bayesian approach to the discovery of causal models, using a Minimum Message Length (MML) method. We have developed encoding and search methods for discovering linear causal models. The initial experimental results presented in this paper show that the MML induction approach can recover causal models from generated data which are quite accurate reflections of the original models; our results compare favorably with those of the TETRAD II program of Spirtes et al. even when their algorithm is supplied with prior temporal information and MML is not.