The paper is concerned with the calculation of the effective diffusivity of transversely isotropic material with spheroidal pores by means of effective field methods. The segregation effect that is the main difference between conductivity and diffusivity problems is taken into account. Wiener's and Hashin-Shtrikman's bounds are modified to account for the segregation. Orientational scatter of pores about a preferential orientation is considered. Mori-Tanaka, Kanaun-Levin, and Maxwell homogenization schemes in terms of property contribution tensors are used. The calculated diffusion coefficients depend on the volume fraction, the shape of pores, their distribution over orientations in a three-dimensional solid, and the segregation factor.