An approach based on cavity compliance contribution tensor is utilized for evaluation of effective stiffness of anisotropic materials with irregularly shaped pores. The shapes considered in the present work were extracted from the X-ray computed microtomography of a carbon/carbon composite sample. The cavity contribution tensors of individual pores were calculated numerically and then employed in the micromechanical modeling procedure. It was shown that presence of pores with total porosity of p = 9.13% results in approximately 20% reduction in the material's Young's moduli. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)