The absorption of radio wave is relevant to electromagnetic interference (EMI) shielding and low observability. The effect of the absorption distance much above the calculated skin depth on the absorption of radio wave (600-2000 MHz) is studied by determining the absorption loss per unit thickness for aluminum sheets of thickness ranging from 0.528 to 2.053 mm. Aluminum is dominantly used for EMI shielding. The absorption loss SEA increases with increasing thickness, such that when the absorption distance x exceeds 1.3 mm, the increase is slight. The distance 1.3 mm corresponds to similar to 500 times the calculated skin depth for x = 0. Furthermore, when x exceeds 1.3 mm, the linear absorption coefficient alpha obtained from SEA/thickness decreases linearly with increasing x. At x below 1.3 mm, alpha decreases with increasing x in a nonlinear non-exponential manner that is not far from linearity and corresponds to much less decrease for the same x than the exponential case. The non-exponential relationship indicates that the skin effect alone cannot explain the observed relationship. The observed high alpha at large x, at which the electric field is low, indicates nonlinear dielectric behavior. The factor beta that relates alpha(2)/alpha(1) and x(1)/x(2) (where alpha(1) is the alpha value at x(1), and alpha(2) is the alpha value at x(2)) increases with x and levels off at similar to 1.5 when x exceeds 1.3 mm. The effect of x on alpha is large compared to the effect of the frequency on alpha.