A cellular automaton model with threshold elements, previously proposed by Bak et al. <1988>, which generates 1/f noise and self-organizes into a critical state, is studied as a model for earthquake occurrence. The model explains some of fractal features of earthquakes such as the power law distribution of the size of the earthquake. The model is modified so that every earthquake may trigger aftershocks. The modified trigger model explains other fractal features of earthquakes, such as the power law decay of aftershock frequency and the power law correlation of the hypocenter distribution. ¿ American Geophysical Union 1990