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Thermoset polymer composites show promise for additive manufacturing (AM) applications to address some of the limitations of the more widely used thermoplastic feedstock materials. Thermosets offer attractive mechanical properties while providing excellent interlayer bonding, high thermal and chemical stability, and reduced energy consumption as a result of deposition at room temperature. However, since thermoset resins rely on a crosslinking reaction to solidify, rather than quickly cooling like thermoplastics, viscoelastic properties must be relied upon to maintain deposited shape after deposition until crosslinking can occur. This fact has not impeded development and characterization of new thermoset feedstocks on the small scale, but recent efforts to increase scale of thermoset printing have highlighted issues with structural stability under self-weight. This study addresses issues of self-weight by investigating the mechanisms that cause collapse of tall, thin printed walls. Using nanoclay- and fumed silica-filled epoxy feedstocks, this work compares the collapse height for printed walls to stability models based on yielding and buckling mechanics. Inputs for these models – shear yield stress and storage modulus – were taken directly from parallel plate rheometry measurements. Model predictions were found to be in good agreement with experimental results, where both yielding and buckling behavior were observed, provided the rheological properties after a shear excursion were used as inputs. This work establishes a direct link between basic rheological properties of the feedstock, geometry of the printed object, and achievable height. The results presented highlight the importance of understanding recovery behavior in thermoset feedstocks and provide valuable guidance on the development of more effective direct-ink writing feedstock materials.