The goal of this study is to identify vocal fold geometric and mechanical conditions that are likely to produce large contact pressure and thus high risk of vocal fold injury. Using a three-dimensional computational model of phonation, parametric simulations are performed with co-variations in vocal fold geometry and stiffness, with and without a vocal tract. For each simulation, the peak contact pressure is calculated. The results show that the subglottal pressure and the transverse stiffness of the vocal folds in the coronal plane have the largest and most consistent effect on the peak contact pressure, indicating the importance of maintaining a balance between the subglottal pressure and transverse stiffness to avoiding vocal fold injury. The presence of a vocal tract generally increases the peak contact pressure, particularly for an open-mouth vocal tract configuration. While a low degree of vocal fold approximation significantly reduces vocal fold contact pressure, for conditions of moderate and tight vocal fold approximation changes in vocal fold approximation may increase or decrease the peak contact pressure. The effects of the medial surface thickness and vocal fold stiffness along the anterior-posterior direction are similarly inconsistent and vary depending on other control parameters and the vocal tract configuration.