FRANC3D is a program for simulating arbitrary three-dimensional crack growth. Recently, a completely new version of the program, FRANC3D/NG, has been created. Unlike previous versions, which relied largely on boundary element analysis, the new version of the program works with finite element analysis exclusively and is designed to work with general-purpose commercial finite element packages. This paper presents the theoretical underpinnings of the procedures to adaptively modify the geometry and mesh of a model to simulate crack growth.