An approximate model based on the so-called "second-order" nonlinear homogenization method is proposed to estimate the effective behavior of viscoplastic porous materials exhibiting transversely isotropic symmetry. The model is constructed in such a way that it reproduces exactly the behavior of a "composite-cylinder assemblage" in the limit of in-plane hydrostatic loading, and therefore coincides with the hydrostatic limit of Gurson's criterion for plastic porous materials. As a consequence, the new model improves on earlier "second-order" homogenization estimates, which have been found to be overly stiff at sufficiently high triaxialities and nonlinearities. The proposed model is compared with exact results obtained for a special class of porous materials with sequentially laminated microstructures. The agreement is found to be excellent for the entire range of stress triaxialities, and all values of the porosity and nonlinearity considered.