Many influential memory models are computational in the sense that their predictions are derived through simulation. This means that it is difficult or impossible to write down a probability distribution or likelihood that characterizes the random behavior of the data as a function of the model’s parameters. In turn, the lack of a likelihood means that these models cannot be directly fitted to data using traditional techniques. In particular, standard Bayesian analyses of such models are impossible. In this article, we examine how a new procedure called approximate Bayesian computation (ABC), a method for Bayesian analysis that circumvents the evaluation of the likelihood, can be used to fit computational models to memory data. In particular, we investigate the bind cue decide model of episodic memory (Dennis & Humphreys, 2001) and the retrieving effectively from memory model (Shiffrin & Steyvers, 1997). We fit hierarchical versions of each model to the data of Dennis, Lee, and Kinnell (2008) and Kinnell and Dennis (2012). The ABC analysis permits us to explore the relationships between the parameters in each model as well as evaluate their relative fits to data—analyses that were not previously possible.