The purpose of the present work was to define some parameters of compatibility between the titanium nanotubes surface and the human cells layer. The nanotube-matrix interphase provided the necessary information concerning the possibility of compatibility between a titanium prosthesis and human tissue. An important point of view was the biomechanical response of the interphase created by the surfaces involved (interface modelling). The viscoelastic hybrid interphase model developed for the determination of the interphasial stress and strain fields as well as for the prediction of the stiffness variation within the area of the interphase material has been applied in the special case of a substrate containing human osteoblasts and the pure titanium surface covered with titanium nanotubes. The results showed that in order to achieve a strong fixation of the metal to the tissue while at the same time to develop a good environment for the development of the osteoblast cells, extreme values corresponding to both, perfect adhesion or zero adhesion, should be excluded. It was found that the optimum condition is achieved for nanotube-matrix adhesion factor 'k' of intermediate value. (C) Koninklijke Brill NV, Leiden, 2011