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Next point-of-interest (POI) recommendation aims to offer suggestions on which POI to visit next, given a user's POI visit history. This problem has a wide application in the tourism industry, and it is gaining an increasing interest as more POI check-in data become available. The problem is often modeled as a sequential recommendation problem to take advantage of the sequential patterns of user check-ins, e.g., people tend to visit Central Park after The Metropolitan Museum of Art in New York City. Recently, self-attentive networks have been shown to be both effective and efficient in general sequential recommendation problems, e.g., to recommend products, video games, or movies. Directly adopting self-attentive networks for next POI recommendation, however, may produce sub-optimal recommendations. This is because vanilla self-attentive networks do not consider the spatial and temporal patterns of user check-ins, which are two critical features in next POI recommendation. To address this limitation, in this paper, we propose a model named SANST that incorporates spatio-temporal patterns of user check-ins into self-attentive networks. To incorporate the spatial patterns, we encode the relative positions of POIs into their embeddings before feeding the embeddings into the self-attentive network. To incorporate the temporal patterns, we discretize the time of POI check-ins and model the temporal relationship between POI check-ins by a relation-aware self-attention module. We evaluate the performance of our SANST model with three real-world datasets. The results show that SANST consistently outperforms the state-of-theart models, and the advantage in nDCG@10 is up to 13.65%.