To provide a method by which the surface of an aluminum or aluminum alloy material is converted into a three-dimensional crystalline pattern having high metallic luster and decorativeness.

The method is disclosed for producing an aluminum or aluminum alloy material which has a surface provided with many indeterminate crystal patterns having a polygonal shape, a circular shape, a semicircular shape, a belt shape, a radial shape or their combined shape with an area of ≥1 mm2, and which has level difference in a height of ≥10 μm, preferably of ≥20 μm in the boundary of each crystalline pattern, wherein an aluminum alloy material is subjected to such level difference type crystal precipitation treatment that the aluminum alloy material is dipped in a solution of the hydroxide of alkali metal and/or alkaline-earth metal and an additive at 70 to 95°C once or twice for the total time of 6 to 30 min, and the aluminum alloy material is next subjected to anodic oxidation treatment, PVD or CVD treatment.