Summary: A general method combining the volume averaging technique and image analysis is proposed to determine the effective thermal conductivity tensor of real fibrous materials featuring local anisotropic thermal properties. The application of mathematical morphology tools on 3D images of wood based fibrous insulators allows a thorough investigation of the microstructure of these materials. A representative elementary volume is determined and the geometrical structure and local anisotropy are studied and quantified. The classical closure problem coming from the one equation model is solved on the 3D thermal conductivity tensor field and the effective thermal conductivity is computed. Good agreement with available experimental data is achieved.