Noncontacting mechanical face seals are often described as unpredictable machine elements, gaining this moniker from numerous instances of premature and unexpected failure. Machine faults such as misalignment or imbalance exacerbate seal vibration, leading to undesirable and unforeseen contact between the seal faces. A hypothesis explaining the high probability of failure in noncontacting mechanical face seals is this undesired seal face contact. However, research supporting this hypothesis is heuristic and experiential and lacks the rigor provided by robust simulation incorporating contact into the seal dynamics. Here, recent developments in modeling rotor–stator rub using rough surface contact are employed to simulate impact phenomena in a flexibly mounted stator (FMS) mechanical face seal designed to operate in a noncontacting regime. Specifically, the elastoplastic Jackson–Green rough surface contact model is used to quantify the contact forces using real and measurable surface and material parameters. This method also ensures that the seal face clearance remains positive, thus allowing one to calculate fluid-film forces. The seal equations of motion are simulated to indicate several modes of contacting operation, where contact is identified using waveforms, frequency spectra, and contact force calculations. Interestingly, and for the first time, certain parameters generating contact are shown to induce aperiodic mechanical face seal vibration, which is a useful machine vibration monitoring symptom. Also for the first time, this work analytically shows a mechanism where severe contact precipitates seal failure, which was previously known only through intuition and/or experience. The utility of seal face contact diagnostics is discussed along with directions for future work.