Acoustic signals that are stable across a range of articulatory parameters have been suggested as an important feature of speech production [Stevens 1989, J. Phonetics, 17, 3-45]. These so-called quantal effects have also been suggested to arise from the biomechanics of the vocal tract [Fujimura 1989, J. Phonetics, 17, 87-90; Gick & Stavness 2013, Front Psychol 4, 977]. Assessment of potential biomechanical-acoustic quantal relations is hampered by the difficulty of measuring biomechanical parameters, such as muscle excitations, during speech production. Computer modeling has been widely used to probe vocal tract biomechanics, but previous modeling studies have been limited to a small number of deterministic simulations [Gick et al. 2014, CMBBE Imag Vis., 2, 217-22]. We propose a novel probabilistic simulation framework in order to assess how variation in speech motor signals manifests in acoustic variation. We use a detailed 3D biomechanical model of the vocal tract coupled to a source-filter acoustics model [Stavness et al. 2014, Siggraph Asia Tech, 9] in order to generate acoustic output from muscle excitation inputs. Monte Carlo sampling of muscle excitation inputs are used to characterize variation in formant frequencies for vowel production. These large-scale simulations permit us to evaluate the hypothesis that quantal acoustic signals originate from regions of biomechanical stability. If found, quantal biomechanical-acoustic relations would provide a simple, principled mechanism for feedforward control of speech production.