A phenomenological model is proposed for calculating the volumetric (VEI) and radial (SEI) expansion indices, and the anisotropy factor of extruded starch from the melt shear viscosity (η). The model parameters depend on the moisture content (MC), the specific mechanical energy (SME), the melt temperature (T) and the melt storage modulus (E′). The latter represents the contribution of the elongational viscosity. The model is developed using a large data-set covering a wide range of thermomechanical conditions and rheological properties. The cellular structure is also predicted by linking the anisotropy factor to the cellular fineness (F). The model is validated using both a specific validation data-set and data taken from the literature. The simulation results show that η, MC and T influence negatively VEI and positively F, while E’ positively affects both properties. These trends make it possible to adjust the structure of the extruded starches by selecting appropriate processing conditions. Finally, an optimization method based on overlaid contour plots is applied to determine the range of input variables leading to a targeted cellular structure.