In human voice production (phonation), linear small-amplitude vocal fold oscillation occurs only under restricted conditions. Physiologically, phonation more often involves large-amplitude oscillation associated with tissue stresses and strains beyond their linear viscoelastic limits, particularly in the lamina propria extracellular matrix (ECM). This study reports some preliminary measurements of tissue deformation and failure response of the vocal fold ECM under large-strain shear The primary goal was to formulate and test a novel constitutive model for vocal fold tissue failure, based on a standard-linear cohesive-zone (SL-CZ) approach. Tissue specimens of the sheep vocal fold mucosa were subjected to torsional deformation in vitro, at constant strain rates corresponding to twist rates of 0.01, 0.1, and 1.0 rad/s. The vocal fold ECM demonstrated nonlinear stress-strain and rate-dependent failure response with a failure strain as low as 0.40 rad. A finite-element implementation of the SL-CZ model was capable of capturing the rate dependence in these preliminary data, demonstrating the model's potential for describing tissue failure. Further studies with additional tissue specimens and model improvements are needed to better understand vocal fold tissue failure.