This book constitutes the refereed conference proceedings of the 7th International Conference on Finite Difference Methods, FDM 2018, held in Lozenetz, Bulgaria, in June 2018. The 69 revised full papers presented together with 11 invited papers were carefully reviewed and selected from 94 submissions. They deal with many modern and new numerical techniques like splitting techniques, Green’s function method, multigrid methods, and immersed interface method.