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Abstract Material extrusion is popular for its low barriers to entry and the flexibility it gives designers relative to traditional manufacturing techniques. Material extrusion is a transient process with a high frequency of starts, stops, and accelerations. This work presents transient data collected by an instrumented printhead and models the data by way of system identification. First-order and second-order control system models are proposed. The work also includes principal component analysis to determine which model coefficients correlate with the main effect, models the first-order model coefficients as a function of the experimental factors by regression, and predicts the apparent viscosity using a fitted static gain and known parameters. Flow rate, hot end temperature, nozzle diameter, and acceleration are the factors selected for the experiment. Each of these factors influences the steady state pressure, except for acceleration. The system identification models predict the melt pressure’s transient behavior well, with standard errors less than 4% of the mean melt pressure. Statistical analysis of the first-order model coefficients verifies that the static gain and time constant are statistically significant responses of the factors. The modeled apparent viscosity follows rheological expectations, showing the trends typically seen for viscosity as a function of shear rate.