The development of accurate and explicable machine learning models to predict the properties of topologically complex systems is a challenge in material science. Porous organic cages, a class of polycyclic molecular materials, have potential application in molecular separations, catalysis and encapsulation. For most applications of porous organic cages, having a permanent internal cavity in the absence of solvent, a property termed “shape persistency” is critical. Here, we report the development of Graph Neural Networks (GNNs) to predict the shape persistence of organic cages. Graph neural networks are a class of neural networks where the data, in our case that of organic cages, are represented by graphs. The performance of the GNN models was measured against a previously reported computational database of organic cages formed through a range of [4+6] reactions with a variety of reaction chemistries. The reported GNNs have an improved prediction accuracy and transferability compared to random forest predictions. Apart from the improvement in predictive power, we explored the explicability of the GNNs by computing the integrated gradient of the GNN input. The contribution of monomers and molecular fragments to the shape persistence of the organic cages could be quantitatively evaluated with integrated gradient. With the added explicability of the GNNs, it is possible not only to accurately predict the property of organic materials, but also to interpret the predictions of the deep learning models and provide structural insights to the discovery of future materials.