The material extrusion process is one of the most popular additive manufacturing processes. The presence of porosity in the MEX printed parts, which ultimately deteriorates the mechanical properties, is one of the main drawbacks of the MEX process. The porosity in the structure is related to the shape of the adjacent beads and overlapping during the material deposition. Due to the deposition nature of the MEX process, the porosity cannot be entirely removed from the printed parts. Understanding the influence of process parameters on material deposition and the rheological properties is crucial to improving the quality of the final product. In this study, the two-phase-flow numerical approach with the level-set equations has been used for the first time to model the material deposition on the moving platform in 3D. The influence of the viscosity and printing parameters, including travel speed, inlet velocity, viscosity, nozzle diameter, and layer height, on the width of the deposited bead has been investigated. The simulation results are validated against experimental measurements with an average error of 5.92%. The width measured by the experimental study shows good agreement with the results of the numerical simulation. The comparison between the results of the 3D numerical simulation and 2D simulation reveals that the 2D simulation is not appropriate and accurate enough to predict the geometry of the deposited bead with the given set of parameter settings. The key novelty of this research paper is the application of the level-set method in a 3D context for material deposition on a moving substrate.