The P,T-diagram for aluminium hydride obtained at pressures 0.5-6.5 GPa and temperatures 100-700 degrees C indicates that the decomposition of AlH3 is reversed at high pressures and the compound can be prepared from the elements at pressures above 2.5 Gpa. However, synthesis of AlH3 via the solid-state exchange reactions of LiAlH4 or LiH with AlCl3 under quasi-hydrostatic conditions is more advantageous. The synthetic P,T-conditions are limited by two straight lines that correspond to the decomposition of AlH3 into elements and the phase transition alpha-LiAlH4 --> beta-LiAlH4. Similar reaction of alpha-LiAlH4 with aluminium chloride does not occur at all, while reactions with alpha- and beta-Li3AlH6 lead to complete decomposition of the starting compounds. The reaction of AlCl3 with LiH to give AlH3 proceeds only at P > 5.6 GPa and T > 550 degrees C. Only the most compact cr (hexagonal) modification of AlH3 is formed under the P,T-conditions studied.