A 3D biomechanical model of the tongue and the oral cavity, controlled by a functional model of muscle force generation (-model of the equilibrium point hypothesis) and coupled with an acoustic model, was exploited to study the activation of the tongue and mouth floor muscles during the production of French cardinal vowels. The selection of the motor commands to control the tongue and the mouth floor muscles was based on literature data, such as electromyographic (EMG), electropalatographic (EPG) and cineradiographic data. The tongue shapes were also compared to data obtained from the speaker used to build the model. 3D modeling offered the opportunity to investigate the role of the transversalis, in particular its involvement in the production of high front vowels. It was found, with this model, to be indirect via reflex mechanisms due to the activation of surrounding muscles, not voluntary. For vowel /i/, local motor command variations for the main tongue muscles revealed a non-negligible modification of the alveolar groove in contradiction to the saturation effect hypothesis, due to the role of the anterior genioglossus. Finally, the impact of subject position (supine or upright) on the production of French cardinal vowels was explored and found to be negligible.