A previous bone remodelling model was presented elsewhere [30], and in the present paper, the same model was tested with new conditions; an interaction between bone tissue, bone substitute material and a dental implant was considered. The bone substitute material was assumed to be dead tissue, which does not synthesizes neither absorbs bone tissue, and it was considered, as well, resolvable. A moving border between the bone substitute material and the bone tissue was studied. The border moved as the newly synthesised bone tissue took over the bone substitute material. After the numerical calculations of time-steps, the whole bone substitute material was replaced by normal bone tissue and the implant was fixed in place only by bone tissue. Dynamical studies of the interaction of bone tissue and implant are used to improved implant design considering different factors, in this case, the presence of bone substitute material helping to fix the implant.