Despite the use of paste extrusion to make a wide range of products, process design and operation can often be compromised by the occurrence of flow instabilities. These are manifest as surface fractures of a number of different types. Here, direct observations of a two-dimensional flow through transparent walls show, for the first time, that these fractures originate in the development of cracks first on one side and then on the other in the paste around the die exit. These fractures can occur in the region immediately prior to the exit, or they can arise directly at the exit. This behavior is consistent with numerical predictions of stresses at the exit, which reveal tension at the surface. Stress distribution, crack initiation, and crack growth to form surface fractures, together with the relationship of these factors to the paste formulation, raise important questions for the future.