The effect of internal architecture on the mechanical properties of stochastic honeycombs was investigated by using four polypropylenes with varying rheological properties. The polymers were first characterized in terms of their thermal and mechanical properties, and then used to fabricate a set of stochastic honeycombs over a range of densities. The internal architecture was characterized by X-ray tomography, and the out-of-plane compressive properties of the stochastic honeycombs were determined. Overall, the strengths varied from 1 to 4 MPa over a core density range of 7-14 %. A thin-plate buckling model was developed to build a predictive strength model. This model was split into a material properties portion (dependent on the polymer stiffness) and an architectural portion (dependent on the fraction of bound webs in the honeycomb). The model was found to serve as a good first step towards predicting the strength of irregular honeycombs.