This book constitutes the refereed proceedings of the 13th International Conference on Reachability Problems, RP 2019, held in Brussels, Belgium, in September 2019.The 14 full papers presented were carefully reviewed and selected from 26 submissions. The papers cover topics such as reachability for infinite state systems; rewriting systems; reachability analysis in counter/timed/cellular/communicating automata; Petri nets; computational aspects of semigroups, groups, and rings; reachability in dynamical and hybrid systems; frontiers between decidable and undecidable reachability problems; complexity and decidability aspects; predictability in iterative maps; and new computational paradigms.