Extrusion is a widely used process for forming suspensions and pastes into designed shapes, and is central to the manufacture of many products. In this article, the extrusion through a square-entry die of non-Brownian spheres suspended in Newtonian fluid is investigated using discrete element simulations, capturing individual particle-particle contacts and hydrodynamic interactions. The simulations reveal inhomogeneous velocity and stress distributions, originating in the inherent microstructure formed by the constituent particles. Such features are shown to be relevant to generic paste extrusion behavior, such as extrudate swell. The pressure drop across the extruder is correlated with the extrudate flow rate, with the empirical fitting parameters being linked directly to particle properties such as surface friction, and processing conditions such as extruder wall roughness. Our model and results bring recent advances in suspension rheology into an industrial setting, laying foundations for future model development, predictive paste formulation and extrusion design. © 2016 American Institute of Chemical Engineers AIChE J, 63: 3069–3082, 2017