This paper presents our experimentation and modeling efforts to study the pattern of material flow in the extrusion and deposition stages of the Contour Crafting (CC) process. Specifically, we performed a preliminary finite element analysis (FEA) of extrusion and deposition mechanisms with clay as the fabrication material. Using the FEA simulations, we derived certain basic understandings of the effect of extrusion orifice geometry on the performance of CC. We found that a square orifice is most aptly suited, both in terms of delivering the optimal fusion between layers as well as creating the desired external surface profile. Our experiments validate these results.