Personal identity continuity has been a focus of much philosophical inquiry, yet lay perceptions of identity continuity and their psychological bases are not well understood. We hypothesize that cultural differences in lay beliefs about the fixedness of the world promote different intuitions about identity continuity: People from a society with rigid social systems should perceive more identity discontinuity when a person’s social relationships (vs. internal traits) change, whereas those from a society with more flexible social systems should perceive the reverse. We tested this hypothesis by comparing fixed-world beliefs and perceptions of identity discontinuity in India and the United States. Results of two studies (N = 863) showed that Indians perceived more identity discontinuity than Americans when relationships (vs. internal traits) changed, which was explained by Indians’ stronger fixed-world beliefs. Moreover, in Study 2, cultural differences in perceived identity discontinuity mediated cultural differences in trust when a target’s relationships (vs. internal traits) changed.