Purpose This paper aims to develop experimentally validated numerical models to accurately characterize the cross-sectional geometry of the deposited beads in a fused filament fabrication (FFF) process under various process conditions. Design/methodology/approach The presented numerical model is investigated under various fidelity with varying computational complexity. To this end, comparisons between the Newtonian, non-newtonian, isothermal and non-isothermal computational models are presented for the extrusion of polylactic acid material in an FFF process. The computational model is validated through an experimental study on an off-the-shelf FFF printer. Microscope images of experimentally printed FFF bead cross-sections corresponding to various printing conditions are digitally processed for the validation. In the experimental study, common practical printing conditions for an FFF process are tested, and the results are compared to the numerical model. Findings Microscope image analyses of the cross-sectional geometries of deposited beads show that the numerical model provides a precise characterization of the cross-sectional geometry under varying process parameters in terms of the cross-section outline, bead height and width. The results show that the nozzle-to-table distance has a great effect on the bead shape when compared to the extrusion rate at a given nozzle-to-table distance. Comparison of the various computational models show that the non-Newtonian isothermal model provides the best tradeoff between computational complexity and model accuracy. Originality/value The authors provide detailed computational models, including the extruder nozzle geometry for cases ranging from Newtonian isothermal models to non-Newtonian non-isothermal models with experimental validation. The validation study is conducted for practical process parameters that are commonly used in FFF in practice and show that the computational models provide an accurate depiction of the true process outputs. As the developed models can accurately predict process outputs, they can be used in further applications for process planning and parameter tuning.