This book constitutes the proceedings of the 18th International Conference on Reachability Problems, RP 2024, which took place in Vienna, Austria, during September 25-27, 2024. The 13 full papers included in these proceedings were carefully reviewed and selected from 37 submissions. The book also contains two invited talks in full paper length. The contributions in these proceedings cover topics from computability and reachability; automata and complexity; linear systems and recurrences; and games and abstractions.