This article introduces an agent-based and a system-dynamics model investigating the cultural transmission of frequent collective rituals. It focuses on social function and cognitive attraction as independently affecting transmission. The models focus on the historical context of early Christian meals, where various theoretically inspiring trends in cultural transmission of rituals can be observed. The primary purpose of the article is to contribute to theorizing about cultural transmission of rituals by suggesting a clear operationalization of their social function and cognitive attraction. (...) Furthermore, the article challenges recent trends in the field by providing a theoretically feasible model for how, under certain conditions, cognitive attraction can influence the transmission to a relatively greater extent than social function. In the system dynamics model we reproduce the results of our agent-based model while putting some of our basic operational assumptions under scrutiny. We consider approaching social function and cognitive attraction in isolation as a preliminary but necessary step in the process of creating more complex models of the cultural selection of rituals, where the two aspects will be combined to produce ritual forms with greater correspondence to real-world religious rituals. (shrink)