The enormous computational power and time required for simulating the complex phonation process preclude the effective clinical use of computational larynx models. The aim of this study was to evaluate the potential of a numerical larynx model, considering the computational time and resources required. Using Large Eddy Simulations (LES) in a 3D numerical larynx model with prescribed motion of vocal folds, the complicated fluid-structure interaction problem in phonation was reduced to a pure flow simulation with moving boundaries. The simulated laryngeal flow field is in good agreement with the experimental results obtained from authors’ synthetic larynx model. By systematically decreasing the spatial and temporal resolutions of the numerical model and optimizing the computational resources of the simulations, the elapsed simulation time was reduced by 90% to less than 70 h for 10 oscillation cycles of the vocal folds. The proposed computational larynx model with reduced mesh resolution is still able to capture the essential laryngeal flow characteristics and produce results with sufficiently good accuracy in a significant shorter time-to-solution. The reduction in computational time achieved is a promising step towards the clinical application of these computational larynx models in the near future.