The aim of this presentation is to extend recent works devoted to the study of the effect of 3D pores of concave shape embedded in isotropic matrix to the case of transversely isotropic (TI) matrix. In the first part, we'll present a brief review of numerical calculation of compliance contribution tensors (which have been introduced in this seminar last year). Then, the approximate relations for the compliance contribution tensor of pores of two reference shapes, supersphere, and axisymmetrical superspheroid, are developed on the basis of 3D Finite Element Modelling, and known exact solutions for the limiting cases of spherical pores and circular crack. In the last part application to effective elastic coefficients of transversely isotropic materials in the frame of homogenization theory is presented to illustrate the impact of concavity parameter on overall properties.