Summary: In one dimension, asymptotic behaviour of densities of stable distributions is well-known. However, in multi-dimensional cases it is very difficult to investigate asymptotic behaviour of densities of non- degenerate stable distributions in general. We give the following two results: If the Lévy measure of the stable distribution has mass at a half-line, then the density decreases along the half-line with the same order as in the one-dimensional case. If the Lévy measure is supported only on finitely many halflines, then we can determine asymptotic behaviour along each direction starting at 0.