Mechanical face seals are wide spread in many applications of powered equipment and turbomachinery. Often machine vibration and noise are unavoidable because of changing conditions which can be persistent and forceful. In critical applications when seals fail, they may have significant or even catastrophic consequences. To ensure the safety of such machinery and its associated mechanical components, machine vibration and noise must be diagnosed and quantified to keep the system’s response within certain limits. This work focuses on the dynamics of a flexibly mounted stator mechanical face seal that is subjected to combinations of broad-band noisy vibrations of the shaft and the housing. In all previous work, the positions of the housing and the shaft have been considered fixed. The current work relaxes that condition, augmenting the equations of motion to incorporate equipment’s noisy vibrations. Noises are expediently produced by the Weierstrass–Mandelbrot (WM) fractal function. A numerical simulation ensues, and the time-domain responses are subject to spectral analyses. Results show that under some design conditions, the seal is largely insensitive to machine vibrations. However, under other conditions, the seal response to exterior machine noise exhibits a rich spectral content that stems from various transient phenomena that include intensified half-frequency whirl, near synchronous response at steady-state, and super-synchronous higher harmonic oscillations caused by face contact.