The idea that the notion of mechanical procedure can play a crucial theoretical role in the study of human intelligence is extensively discussed in methodological contribution to artificial intelligence and cognitive psychology. An understanding of these methodological discussions presupposes that at least some distinctive properties of the notion of computational theory be relatively clear. This paper is devoted to examining this notion, with the principal aim of pointing out how Turing's thesis enables one to characterize a basic condition for theories in cognitive psychology to count as computational. A characterization of computational is crucial also for judging what might count as an extension of the computational framework for psychological theorizing.