The present paper deals with the micromechanical modeling of the effective thermal conductivity of composite materials containing ellipsoidal inclusions with inter-faces thermal resistance. At these interfaces between inclusions and the surrounding medium, the heat flux is assumed continuous while the temperature field undergoes to a discontinuity. The solution of this problem of heterogeneous thermal conductivity is obtained thanks to a micromechanical approach based on the generalized Eshelby's thermal conductivity tensor and the Kapitza's interface thermal resistance model. Moreover, the present study is conducted in the general case of an anisotropic thermal conductivity of each phase and the inclusions are assumed to have an ellipsoidal shape. Results in terms of the thermal intensity field localization inside each phase are presented and then analyzed in light of the effects of some model parameters. The effective thermal conductivity of the equivalent material has been predicted through classical homogenization schemes such as the Mori Tanaka, the Self-consistent, the Generalized self-consistent and the Differential scheme. The model predictions have been also compared with results provided by previous investigations. (C) 2016 Elsevier Ltd. All rights reserved.