This book constitutes the refereed proceedings of the 10th International Workshop on Reachability Problems, RP 2016, held in Aalborg, Denmark, in September 2016. The 11 full papers presented together with2 invited papers and 3 abstracts of invited talks were carefully reviewed and selected from 18 submissions. The papers cover a range of topics in the field of 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.