Hydroelastic instability of blades in flowing passageway is one of important factors which induce hydraulic vibrations of a huge hydro turbine machinery. An objective of this paper is to establish a mathematical methodology to analyze the characteristics of the dynamical instability of the blades of huge Francis Hydro Turbine. To do that, theory of the arbitrary thin shell and arbitrary Lagrangian-Eulerian (ALE) formulation are applied in an orthogonal streamlines coordinate system to get a nonlinear parametric model describing vibration along the normal of the blade surfaces, and the dynamical instability conditions on the Bessel function expansion with the frictional velocity in the near-walled region of the blade was obtained.