A novel tree-like branching network with polygonal loops is designed based on the network of leaf vein. In this study, analytical models are presented for the effective permeabilities through the undamaged and damaged tree-like branching networks with polygonal loops based on Hagen-Poiseuille equation and Darcy's law. These effective permeability models are explicitly related to the structural parameters and the damaged number (or points) of the tree-like branching networks. We have discussed quantitatively the influences of the length and diameter ratios of channels, Y-shaped bifurcation angle, total branching level number, and damaged number (or points) on the effective permeability. Besides, numerical simulations are performed, and compared with the model predictions. Good agreement indicates that the present models for the permeability are reasonable. These analyses of the networks may provide a basis for scientific and engineering applications. (C) 2019 Elsevier Ltd. All rights reserved.