This book constitutes the proceedings of the 10th International Workshop on Numerical Software Verification, NSV 2017, held in Heidelberg, Germany, in July 2017 - colocated with the International Workshop on Formal Methods for Rigorous Systems Engineering of Cyber-Physical Systems, RISE4CPS 2017, a one-time, invited-only event.The 3 full papers presented together with 3 short papers, 2 keynote abstracts and 4 invited abstracts were carefully reviewed and selected from numerous submissions.The NSV 2017 workshop is dedicated to the development of logical and mathematical techniques for the reasoning about programmability and reliability.