The continuous infall of dark matter with low velocity dispersion from all directions in a galactic halo leads to the formation of caustics which are very small scale ({approx}parsec) high density structures. If the dark matter is made up of supersymmetric neutralinos, the annihilation of these particles produces a characteristic spectrum of gamma rays which, in principle, could be detected. The annihilation signal at different energy bands is computed and compared with the expected gamma ray background.