A stripe-shaped cavity structure was formed with amorphous alumina membrane on a sapphire substrate and its solid phase epitaxy (SPE) to crystalline sapphire membrane was investigated by transmission electron microscopy (TEM). The SPE process occurred through two-stage phase transformation from amorphous to gamma-Al2O3 and subsequently to alpha-Al2O3. SPE of gamma-Al2O3 at around 780 degrees C was initiated from the interface between amorphous alumina and sapphire substrate with an epitaxial relationship of [0 0 0 1](sapphlre)//[1 1 1](gamma-Al2O3). Besides SPE, it was observed that nanocrystalline gamma-Al2O3 were formed in the upper part of the membrane after an incubation time. The subsequent phase transformation of the alumina membrane from gamma- to alpha- Al2O3 was observed at higher temperatures above 920 degrees C. The SPE of alpha-Al2O3 began at the corner region of the membrane and proceeded along the whole membrane. The whole alumina membrane was successfully transformed into single crystalline alpha-Al2O3 by SPE after annealing at 1063 degrees C for 2.5 h. The SPE kinetics was investigated by precise measurement of the thicknesses of epitaxially transformed gamma- and alpha-Al2O3 layers in TEM images, resulting in activation energies of 3.1 eV and 3.9 eV for the SPE from amorphous to gamma-phase and that from gamma- to alpha-phase, respectively.