Simulating the flow-induced vibration of structures is fraught with uncertainty. Not only are structural parameters like boundary conditions and damping notoriously uncertain, but the flow induced forces are even more so. The two main approaches for estimating uncertainty are sensitivity-based and stochastic-based. Sensitivities of an output variable, such as surface-averaged vibration, with respect to uncertain inputs, such as damping or flow velocity, may be computed analytically, or numerically using finite differencing techniques. The sensitivities are combined with assumed input variable uncertainty distributions to estimate output uncertainty. The sensitivity-based method works well when the uncertainties are not cross-coupled. For flow-induced vibration, however, there are several inter-dependencies. For example, flow induced forces change with frequency, and if a structural resonance frequency is uncertain the overall uncertainty depends on the combination of structural and flow input parameters. In coupled uncertainty cases stochastic methods are simpler to apply. Uncertainty ranges and distributions, such as normal, uniform, lognormal, or others are assumed for each uncertain input. An n-dimensional random distribution of possible inputs, spanning all structural and flow input parameters, is generated and the simulation executed repeatedly for each set of inputs. The output response distributions are then available to plot and examine, along with global sensitivities—which show which input variables have the most impact on the output variability. In this paper I demonstrate these uncertainty principles on the vibration of Blake and Maga’s cantilevered strut excited by turbulence ingestion flow in a water tunnel. I examine uncertainty in structural parameters which affect resonance frequency and hydrodynamic damping (a cross-coupled uncertainty!) and flow parameters like mean velocity, turbulence intensity, and integral length scale. The simulated vibrations at resonance, spanned by the resulting uncertainties [computed using a Microsoft Excel plugin called Argo from Booz Allen Hamilton agree well with measurements.