The nozzle pressure was monitored in a fused filament fabrication process for the printing of high impact polystyrene. The contact pressure, defined as the pressure applied by the newly deposited layer onto the previous layer, is experimentally calculated as the difference between the pressure during printing and open discharge at the same volumetric flow rates. An analytical method for estimating the contact pressure, assuming one-dimensional steady isothermal flow, is derived for the Newtonian, power-law, and Cross model dependence of shear rates. A design of experiments was performed to characterize the contact pressure as a function of the road width, road height, and print speed. Statistical analysis of the results suggests that the contribution of the pressure driven flow is about twice that of the drag flow in determining contact pressure, which together describe about 60% of the variation in the observed contact pressure behavior. Modeling of the elastic and normal stresses at the nozzle orifice explains an additional 30% of the observed behavior, indicating that careful rheological modeling is required to successfully predict contact pressure.