The fracture investigations of the planar lattices made of ductile cell walls are cur-rently limited to bending-dominated hexagonal honeycomb. In this paper, the plastic zones of stretching-dominated lattices, including Kagome and triangular lattices, are estimated by ana-lyzing their effective yield loci. The normalized in-plane yield loci of these two lattices are almost identical convex curves enclosed by 4 straight lines, which is almost independent of the relative density but is highly sensitive to the principal stress directions. Therefore, the plastic zones around the crack tip of Kagome and triangular are estimated to be quite different to those of the con-tinuum solid and also hexagonal lattice. The plastic zones predictions by convex yield surfaces of both lattices are validated by FE calculations, although the shear lag region caused by non-local bending effect in the Kagome lattice enlarges the plastic zone in cases of small ratio of Tp/l.