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Elucidation of the geometric signs in Upper Palaeolithic art is hampered by an absence of directly relevant ethnography and by the logical impossibility of inducing meaning from numerical rock-art data. This paper approaches the signs by constructing a neuropsychological model of the apprehension of entoptic phenomena in three stages of altered states of consciousness. The utility of the model is assessed by applying it to two known shamanistic rock arts, San and Shoshonean Coso. It is then applied to Upper Palaeolithic mobile and parietal art to show that this art was also associated with altered states of consciousness. Some of the implications of this conclusion for understanding the meaning of entoptic elements, the diverse contexts of Upper Palaeolithic art, the co-occurrence of signs and representational art, and the origins of art are briefly considered.