This paper investigates reduced-order modelling approaches to predict the structural vibrations of an elastic cantilevered hydrofoil in the presence of incident homogeneous and isotropic turbulent flow. The turbulent inflow generates unsteady loading at low frequencies which may lead to excessive noise and structural fatigue. Three methods for calculating the structural excitation caused by the interaction of the hydrofoil leading edge with the free stream turbulence are combined with the hydro elastic equations to investigate the structural vibration velocity and lift response. These are the correlation, the spectrum and the Uncorrelated Wall Plane Wave (UWPW) techniques. Different gust response functions are also investigated that take into account compressible and incompressible skewed gusts and incompressible normal gust. A thickness correction to the gust response function is also incorporated to account for the hydrofoil finite thickness. Finally, the predictions derived from the different methods are compared with available vibration velocity measurements for a cantilevered NACA0015 hydrofoil in grid-generated turbulence. The comparisons and limitations of the different models are discussed.