In this study, we consider the problem of nonlinearly tapered annular plate with a free edge. The supported edge may be simply supported, clamped or elastically restrained against rotation. Exact expressions of deflection, moment-resultants, and stresses are presented for nonuniform thickness. We compare the results of the Kirchhoff plate theory and the Mindlin plate theory. It is shown that the Kirchhoff plate theory and the Mindlin plate theory provide approximately the same results for the positive values of the thickness factor, but the difference between the deflections diverges as the thickness increases at the inner edge. We also propose that the Kirchhoff plate theory may be used in the region of -0.4 <= alpha < 1 and the Mindlin plate theory must be used for alpha < -0.4.