Recent developments have enabled material extrusion additive manufacturing of thermoset-based composite inks on the large scale. In addition, printing out-of-plane components is of broad interest to the polymer material extrusion community. This work addresses some of the challenges associated with both large-scale and out-of-plane thermoset material extrusion additive manufacturing by studying the height at which thin overhanging walls collapse. Walls at a range of overhang angles were printed until they collapsed. An optical camera captured the profile of each wall throughout the print, allowing the collapse height to be identified and the geometric fidelity to the programmed angle to be evaluated. Using previously measured rheological properties, predictive models were generated to approximate the collapse height and profile of the deflected walls. First, an analytical model was created to predict the height at which the walls would yield. The analytical model assumes the walls exhibit a perfectly linear profile; however, experiments proved this assumption to be false. Therefore, a finite element simulation was developed to account for the elastic deflection that occurs during printing. The finite element simulation predicts both the yield height and the deflected profile after the deposition of each layer. For the properties of the thermoset ink used here, the yield height predicted by the analytical model and finite element simulation are virtually identical. These predictions match experimental data reasonably well, but minor errors are observed. Accounting for the fully plastic moment appears to explain the small mismatch between experimental data and predictions. Additionally, the finite element simulation provides an excellent prediction of the deflected profile before the wall begins to collapse. By demonstrating that the collapse height and deflected profile of thin overhanging walls can be predicted, this work illustrates how the soft viscoelastic properties of thermoset-based composite inks limit the scale of a key feature required to print some nonplanar components. It also provides a basis to tailor in-process curing systems to suppress deflection and collapse of thin overhanging walls.