An analytical model is developed for evaluating the eddy current signal from an inspection coil inside a tube under the area of a support plate. The electromagnetic field problem is formulated in terms of the magnetic vector potential and is solved using domain truncation and eigenfunction expansions. Closed-form expressions are derived for the coil impedance and the electromagnetic field. The support plate is effectively replaced by its own surface onto which the Leontovich impedance boundary condition is enforced. The model is quite efficient for the usual configuration that involves a non-ferromagnetic tube and a ferromagnetic support plate and its validity is verified with a commercial FEM package.