Polymer deposition has become widely used in additive manufacturing, particularly in large scale processes where nozzle diameters are on the order of a quarter inch and flow rates in excess of 20 pounds per hour are common. Mechanical and thermal properties of a 3D printed parts produced using polymer extrusion and deposition processes have been shown to improve when adding short carbon fibers to polymer feedstock. As expected, the properties of the fiber-filled polymer composite are significantly influenced by the orientation of the carbon fibers within the extruded bead. Fiber orientation in the bead is affected by the flow field and melt flow geometry, which is defined by the nozzle, extrudate swell, and the turning flow during the polymer composite deposition. In this work, a 2D Stokes flow finite element analysis is performed to evaluate extrusion where special attention is given to the deposition of polymer melt on the moving platform below the nozzle. The shape of the extruded polymer is computed using a free surface normal velocity minimization technique. Once the boundary shape and velocity field are computed, fiber orientation and the resulting mechanical properties of the composite are evaluated throughout the melt flow domain. Fiber alignment is computed using the Advani-Tucker orientation tensor method. Folgar-Tucker isotropic orientation diffusion is employed and results are compared with more recent orthotropic reduced alignment rate techniques. The polymer rheology is modeled in separate simulations as Newtonian, Generalized Newtonian, and viscoelastic. In the latter, both the differential viscoelastic model and the simplified viscoelastic model in ANSYS-Polyflow are used. Results illustrate how contraction in the nozzle, swell at the nozzle exit, and the deposition flow effect fiber orientation and the mechanical properties of the composite. Results are compared for the various orientation diffusion and polymer melt rheology models.