Several theorists have suggested that it is possible to understand and elucidate the moral responsibility of artificial intelligence (AI) agents by using the notion of corporate moral responsibility as a model. We argue that there are differences between corporations and AI agents that make the notion of corporate moral responsibility an inappropriate model for AI agent moral responsibility. We discuss both the moral arguments that purport to show that corporations should or should not be held morally responsible, and the metaphysical arguments that purport to show that a corporation is the kind of entity that can be held morally responsible. We show that these arguments either are wrong or are inapplicable in the context of AI agents.