Abstract - We adapt a constitutive model for the yielding of hydrogels in one-dimensional shear to the elongation-dominated flow in extrusion bioprinting, and develop a finite-element method for computing the morphology and structural evolution in the extrudate. Our numerical simulations capture the main features observed experimentally. In particular, the extrudate show three regions corresponding to unyielded, yielded and degeled states of the bioink. We further develop theoretical estimations for key properties in each of the regions, which agree well with the numerical solutions.