Large language models (LLMs) have exhibited certain indirect pragmatic capabilities, including interpreting indirect requests and non-literal meanings. Yet, it is unclear whether the success of LLMs on pragmatic tasks generalizes to phenomena that directly probe inferences about the beliefs of others. Indeed, LLMs’ performance on Theory of Mind (ToM) tasks is mixed. To date, the most successful computationally explicit approach to making inferences about others’ beliefs is the Rational Speech Act (RSA) framework, a Bayesian probabilistic model that encodes explicit representations of beliefs. In the present study, we ask whether LLMs outperform RSA in predicting human belief inferences, even though they do not explicitly encode belief representations. We focus specifically on projection inferences, a type of inference that directly probes belief attribution. We find that some LLMs are sensitive to factors that affect the inference process similarly to humans, yet there remains variance in human behavior not fully captured by LLMs. The RSA model, on the other hand, outperforms LLMs in capturing the variances in human data, suggesting that explicit belief representation might be necessary to construct human-like projection inferences.